unit 6 precalc apex, unit 10 precalc apex, unit 9 precalc apex, uni 7 precalc apex, unit 8 precalc apex
For the simple harmonic motion equation d=4 sin (8pi*t), what is the maximum displacement from the equilibrium position
4
For the simple harmonic motion equation d=9cos((π/2)t) what is the period
4
Let the function f(x) have the form f(x) = Acos(x + C). To produce a graph that matches the one shown below, what must the value of A be?. A.1. B.3. C.4. D.2
4
what is the amplitude of the sinusoid's graph: y=-4sin3x
4
Convert the following complex number into its polar representation: -4i
4(cos 3pi/2 + isin 3pi/2)
convert the complex number 2-2sqrt3 i into its polar representation
4(cos(300)+isin(300))
Convert the following complex number into its polar representation: 2sqrt 3+2i
4(cos(30°) + i*sin(30°))
Use De Moivre's theorem to write the complex number in standard form. ( sqrt2 (cos(10 degrees)+isin(10 degrees))^6
4+4i*sqrt(3)
What is the period, in seconds, of a simple pendulum of length 5 meters? Use the gravitational constant g = 9.8 m/s2 and round your answer to two decimal places.
4.49
if cos-3/5, then tan=
4/3
Find the quotient of z1 by z2. Express your answer in trigonometric form: z1 = 4(cos(π/3) + isin(π/3)) z2 = 3(cos(2π/5) + isin(2π/5))
4/3 (cos(-π/15) + isin(-π/15))
find the quotient, write your answer in standard form: (3-i)/(3+i)
4/5-3/5i
if z1=5+5i and z2=8(cos(3pi/7)+isin(3pi/7)) then z1 z2=____? A. 8sqrt5(cos(19pi/28)+isin(19pi/28)) B. 40sqrt2(cos(3pi/28)+isin(3pi/28)) C. 40(cos(19pi/28)+isin(19pi/28)) D. 40sqrt2(cos(19pi/28)+isin+(19pi/28))
40sqrt2(cos(19pi/28)+isin+(19pi/28))
Which of the following is not an identity? A. cos^2 x csc x - csc x = -sin x B. sin x(cot x + tan x) = sec x C. cos^2 x - sin^2 x = 1- 2sin^2 x D. csc^2 x + sec^2 x = 1
csc^2 x + sec^2 x = 1
Find a model for simple harmonic motion if the position at t = 0 is 0, the amplitude is 5 centimeters, and the period is 2 seconds
d = 5sin(πt)
Find a model for simple harmonic motion if the position at t = 0 is 6, the amplitude is 6 centimeters, and the period is 4 seconds
d = 6cos(π/2 * t)
Which equation can be used to model simple harmonic motion
d = acos(wt) d = asin(wt)
Find a model for simple harmonic motion if the position at t = 0 is 0, the amplitude is 5 centimeters, and the period is 4 seconds
d=5sin((pi/2)t)
(TRUE or FALSE) When cubing a complex number using De Moivre's theorem, there are three answers.
false
(True or False) All equations are identities, but not all identities are equations.
false
(True or False) The rectangular coordinates of a point are not unique
false
(True or false) The value of r represents the reference angle when plotting a point in polar coordinates
false
(true or false) A rectangular equation that is a function will be a function in any coordinate system
false
(true or false) In this picture, the measure of angle is 1 radian.
false
(true or false) Let f(x) = Tan^-1 x. Then the domain of f(x) is all real numbers and the range (0, pi)
false
(true or false) Let f(x) = cos-1x. Then the domain of f(x) is all real number and the range is [-1,1]
false
(true or false) One disadvantage of polar equations is that you can use a polar function to describe a graph whose equation in rectangular coordinates would not be considered a function
false
(true or false) SSA triangle problems will have either one or two solutions
false
(true or false) Sin(a-b) = sinacosb+cosasinb for all values of a and b
false
(true or false) The Pythagorean theorem is true for all similar triangles
false
(true or false) The expression sin^-1
false
(true or false) The graph of y=4 sin(x+3)-2 is obtained by shifting the graph y=4 sin x-2 horizontally 3 units to the right
false
(true or false) The law of cosines can only be applied to right triangles
false
(true or false) The measure of theta in degrees is approximately 34.38; side lengths are 4, 5.3 ,and 7
false
(true or false) The motion of a pendulum for which the maximum displacement from equilibrium varies is an example of simple harmonic motion
false
(true or false) The notation Arcsin x represents the inverse function to sine.
false
(true or false) There are values of t so that sin t = .3 and cos t = -.6.?
false
(true or false) There are values of t so that the equation cos t= 5/3
false
(true or false) all trigonometric equations are identities
false
(true or false) cosxcosy=1/2(sin(x+y)+sin(x-y))
false
(true or false) tan^2x+sec^2x=1 for all values of x
false
(true or false) tan^2x=(1+cos2x)/(1-cos2x)
false
(true or false) the cosine function is an odd function
false
(true or false) the equation cosx=sqrt3/2 is an identity
false
(true or false) the range of y=arccosx is (-pi/2, pi/2)
false
(true or false) there is no solution for the equation cscx=-1
false
Which description matches the transformations y=cos x undergoes to produce y=3cos (-2x)
horizontal compression by factor 1/2, reflection through the y-axis, then vertical stretch by factor 3
Consider the function y=-2-3cos(x+Pi) what effect does PI have on the basic graph
horizontal shift left pi units
How many possible values for y are there where y = tan ^-1 3 A.1 B.2 C.Infinite D.0
infinite
how many possible values for y are there where y=cos^-10
infinite (i hate math so much)
what is the name of the shape described in the graph (diagonal infinity sign)
lemniscate
what is the name of the shape described below (looks like circle with a smaller circle hugging the edge)
limacon
what is the name of the shape graphed by the function theta=-pi/6
line
what is the name of the shape graphed by the function: theta=-4pi/3
line
A vector has both a direction and a ____. A. Reverse B.Scalar C. Zero D. Magnitude
magnitude
A vector has both a direction and a ____. A. Reverse B.Scalar C. Zero D. Magnitude
magnitude
When a complex number z is written in its polar form,z = r(cos theta + i sin theta) , the nonnegative number r is called the ____________, or modulus, of z.
magnitude
When a complex number z is written in its polar form,z = r(cos theta + i sin theta) , the nonnegative number r is called the ____________ of z.
modulus
The term that describes how long it takes a function to repeat its behavior is the ___
period
at which value will the graph of y=cotx have a zero
pi/2
which value is a solution for the equation tanx/2=1
pi/2
Solve on the interval (0, 2pi): 1-cos theta=1/2
pi/3 , 5pi/3
evaluate tan^-11
pi/4
find all solutions to the equation cos x cos(3x)+sin x sin(3x)=0 on the interval (0,2pi)
pi/4,3pi/4,5pi/4,7pi/4
Solve on the interval (0, 2pi) 1+cos theta=sqrt3 +2/2
pi/6, 11pi/6
In radian measure, the angles of a 45-45-90 triangle are:
pie/4 , pie/4 , pie/2
In polar coordinates, the positive x-axis is called the ___ axis
polar
An equation whose variables are polar coordinates is called a(n) _______________
polar equation
In polar coordinates, the origin is called the _____.
pole
If sin theta < 0 and cos theta > 0, then the terminal point determined by theta is in:
quadrant 4
the graph shown below represents which of the following polar equations
r=3-3sin theta
which equation will produce the graph shown (infinity in middle of graph)
r^2=9cos(2 theta)
check all that apply. if sin=15/17, then
sec=17/8 tan=15/8 csc=17/15
The expression (tanx + cotx)^2 is the same as ___
sec^2x + csc ^2 x
which of the following are not trigonometric identities check all that apply
sec^2x+csc^2x=1 tan^2x+sec^2x=1
_____ pi/3 cos pi/6 = 1/2 (sin pi/2 + sin pi/6)
sin
___ cosb=1/2(sin(a+b)+sin(a-b)
sin a
Which of following are identities. Check all that apply. (sinx-cosx)^(2)=1+sin2x sin8x=2sin4xcos4x (sinx+sin5x)/(cosx+cos5x)=tan3x ((1-tan^(2)x))/(2tanx)=(1)/(tan2x)
sin8x=2sin4xcos4x (sinx+sin5x)/(cosx+cos5x)=tan3x ((1-tan^(2)x))/(2tanx)=(1)/(tan2x)
Which of following is an identity
sin^(2)xcot^(2)x+cos^(2)xtan^(2)x=1
The expression sinx(cscx - cotx cosx) can be simplified to:
sin² x
Suppose a triangle has two sides of length 2 and 5 and that the angle between these two sides is pi/3. What is the length of the third side of the triangle
sqrt 19
Which set of polar coordinates describes the same location as the rectangular coordinates (1,-1)
sqrt 2, 315 degrees
what is the length (magnitude) of the vector (7, -2)
sqrt 53
If sinx = 5/13 and x is in quadrant 1, then sin x /2 = ..... a. - sqrt(5/26) b. sqrt(5/26) c. - sqrt(1/26) d. sqrt(1/26)
sqrt(1/26)
which pair represents the same complex number
sqrt(2)(cos(-(pi )/(4))+isin(-(pi )/(4)))
Which of following are identities. Check all that apply. tan(x-pi)=tanx sin(x+y)+sin(x-y)=2cosxsiny cos(x+y)+cos(x-y)=2cosxcosy cos(x+y)-cos(x-y)=2cosxcosy
tan(x-pi)=tanx cos(x+y)+cos(x-y)=2cosxcosy
A. sin2x - cos2x = 1 B. tan2x = sec2x - 1 C. sin2x = 1 - cos2x D. cot2x + csc2x = 1
tan2x = sec2x - 1 sin2x = 1 - cos2x
(csc(4x)-cot(4x))/(csc(4x)+cot(4x))
tan^2(2x)
which equation is represented by the intersection of the graphs below
tanx=-1
which equation is represented by the intersection of the graphs shown below
tanx=1
Which of the following is an example of simple harmonic motion
the motion of a rotating beacon
Which scenario describes periodic behavior
the movement of a cd in a cd player
Which natural phenomenon is the best example of periodic behavior
the time of sunrise each day
Suppose a triangle has sides 3, 4, and 6. Which of the following must be true? The triangle in question may or may not be a right triangle The triangle in question is not a right triangle The triangle in question is a right triangle
the triangle is not a right triangle
If the dot product of two nonzero vectors v1 and v2 is nonzero, what does this tell us
they are not perpendicular
(TRUE or FALSE) The horizontal distance, in feet, traveled by a projectile can be modeled by the equation.. h = ((v0^2)/16) sinθcosθ ..where θ is the initial angle and v0 is the initial velocity. This simplifies to h = ((v0^2)/32) sin(2θ)
true
(true or false) As long as its argument is restricted to [0,2pi] the polar form of a complex number is unique.
true
(true or false) Cos(a/2) = ± √(1 - cosa)/2 for all values of a
true
(true or false) Cos2a=1-2sin^2a for all values of a.
true
(true or false) De Moivre's theorem is used to raise a complex number to a positive integer power
true
(true or false) In (r, theta), the value of r can be negative.
true
(true or false) Reflecting the graph of y=cosx across the y axis is the same as not reflecting it at all.
true
(true or false) The domain of y = csc x is given by x≠nπ.
true
(true or false) The equation csc^2x-1=cot^2x is an identity
true
(true or false) The law of cosines reduces to the pythagorean theorem for right triangles
true
(true or false) The law of sines can be used to solve triangulation-type problems.
true
(true or false) The range of y=Arcsin x is (-pi/2, pi/2)
true
(true or false) The value 3pi/4 is a solution for the equation 3(sqrt 2) cos theta + 2 = -1
true
(true or false) The value 5pi/2 is a solution for the equation 2sin^2x-sinx-1=0
true
(true or false) The value of r represents the directed distance when plotting a point in polar coordinates
true
(true or false) The value pi/16 is a solution for the equation 2 cos^2(4x)-1=0.
true
(true or false) a function whose values repeat based on positions of a point that moves around a circle is called a sinusoid
true
(true or false) cos 60 =1/2 and sin 60 =sqrt3/2
true
(true or false) cos(x/5)sin(x/5)=1/2(sin(2x/5))
true
(true or false) sec(pi/2-x)=cscx
true
(true or false) sin(-x)=-sin x for all values of x
true
(true or false) sin(75 degrees)=sqrt(1-cos(150 degrees)/2)
true
(true or false) the value 5pi/4 is a solution for the equation 3sqrt2 csc theta+5=-1
true
(true or false) the value pi/24 is a solution for the equation 4cos^2(4x)-3=0
true
(true or false) there is no solution to the equation secx=0
true
(true or false) triangulation is a method of finding the location of an object based on measurements made from two other locations
true
In order to apply the law of sines to find the length of the side of a triangle, it is enough to know which of the following? A. Two angles and a side B. All three angles C. Two sides and one angle D. The area of the triangle
two angles and a side
If the dot product of two nonzero vectors v1 and v2 is zero, what does this tell us
v1 is perpendicular to v2
An equation whose ____ are polar coordinates is called a polar equation
variables
let v=(5,-2) and w=(-10,4). which of the following are true. check all that apply
w=-2v the y component of w is 4 v+w=-58
Assume sin t = .45 and sin w = .89, both t and w are positive, and both t and w determine a terminal point in quadrant 1. Which of the following statements best describes the relationship between t and w?
w>t
which of the following are vertical asymptotes of the function y=3cot(2x)-4 check all that apply
x = 2pi x = +- pi/2 x = pi
which of the following describes the domain of y=secx, where n is any integer
x ≠ (π/2) + nπ
If P(x,y) is the point on the unit circle defined by real number theta, then cotangent of theta = _____.
x/y
solve cos(x)(cos(x)-1)=0
x=pi/2+-2pin, x=3pi/2+-2pin,x=+-2pin
solve cos(x)(cosx+1)=0
x=pi/2+-2pin, x=3pi/2+-2pin,x=+-2pin
Solve on the interval (0, 2pi) (sinx-1)(2sin^2x-5sinx+2)=0
x=pi/2, pi/6, 5pi/6
Solve on the interval (0, 2pi): 2sin^2x-3sinx +1=0?
x=pi/2,pi/6, 5pi/6
find all solutions to the equation secx(2cosx-sqrt2)=0
x=pi/4+2kpi and 7pi/4+2kpi, where k is any positive integer
transform the following polar equation into an equation in rectangular coordinates: r=4
x^2+y^2=16
which of the following functions is NOT a sinusoid
y= Sqrtx
which rectangular equation is equivalent to the polar equation rsin theta=-2
y=-2
which of the following functions illustrates a phase shift
y=-2-cos(x-pi)
Which equation represents the graph of y = cos x flipped across the x-axis then shifted vertically down by 2 units?
y=-cos x-2
choose the function whose graph is given by
y=0.5cosx
choose the function whose graph is given by
y=2sec((1)/(2)x)
which function has the graph shown below
y=3cos(-x)
the graph below represents which of the following functions
y=3cos(2(x+(pi )/(3)))
which functions graph has a period of 2
y=3cospi x
choose the function whose graph is given by
y=3sin(x-2)+1
Fill in the blank. In the triangle below, y = _____. Round your answer to two decimal places. (amgles of 42, 45)
y=47.1
choose the function whose graph is given by
y=4cos(2x)
which of the following are equivalent to the function y=4cosx-2? check all that apply
y=4sin(x+pi/2) - 2 y=4cos(-x)-2
the following graph depicts which inverse trigonometric function
y=arccosx
the following graph depicts which inverse trigonometric function
y=arcsinx
choose the function whose graph is given by
y=cos x-2
choose the function whose graph is given by
y=cos(4x)
choose the function whose graph is given by
y=cos(x+1)
Which graph represents a phase shift of π/2 units left for the graph of y = sinx
y=cosx
which functions graph is shown below
y=cosx
which of the following is a sinusoid
y=cosx
choose the function whose graph is shown below (mutiple lines on graph look like stretched out 2's)
y=cotx
which function has the graph shown below
y=cotx
which function is odd? check all that apply
y=cotx y=cscx y=sinx
which function has the graph shown below
y=csc(x)+1
choose the function whose graph is shown below (lines look like upside down and right side up u's, doesnt pass over y)
y=cscx
which function has the range (-infinty,0) U(2, infinity)
y=sec(x)+1
Which function has a domain of all real numbers except x=pi/2 +- npi?
y=secx
choose the function whose graph is shown below (lines look like upside down and right side up u's, pass directly over y)
y=secx
which of the following have period 2π? check all that apply
y=secx y=cscx
which function has the graph shown below
y=sin(x+pi )
choose the function whose graph is given by
y=sinx-3
the following is the graph of (graph with lines that look likes stretched 5's)
y=tan(2(x-(pi )/(6)))
choose the function whose graph is given by
y=tan(x-pi )-2
choose the function whose graph is shown below (mutiple lines on graph look like stretched out S'es)
y=tanx
When a complex number is written in its polar form, z=r(cos theta + i sin theta) , the angle theta is called the "argument" of _____.
z
Fill in the blank. In the triangle below, z = _____. (angles of 47, 35)
z=43
Which of the following are identities? Check all that apply.
{secx-cosx}/{secx}=sin^2x tanxcosxcscx=1 1-tantany=cos(x-y)/cosxcoy
Check all that apply. (pi/6) is the reference angle for:
π/6 is the reference angle for 5π/6, 7π/6, 11π/6, 13π/6, etc.
the exact value of cos(17pi )/(8)
√(2+√2)/4
The equation tan(x+pi/3) is equal to?
(√3 tanx+1)/(√3-tanx)
Which of the following expressions is a sixth root of unity? 1. i 2. -1 3. -i 4. All of the above are correct
-1
find the exact value of csc(sin^-1(-1)
-1
sin ((19\pi )/(6))
-1/2
If v1= (3, -4) and v2= (2, 6), then v1*v2 is equal to which of the following?
-18
Another representation in polar coordinates of the point is (2,pi/6) is(---,7pi/6)
-2
which set of polar coordinates are plotted in the graph below
-2, 2pi/3
what is the range of the function y=2sinx
-2,2
evaluate the following expression 4(3,5)-2(7,-2)
-2,24
convert the polar representation of this complex number into its regular form: z=4(cos135 degrees+isin135 degrees)
-2sqrt2, 2 sqrt2
convert the polar representation of this complex number into its standard form: z=4(cos 5pi/6+isin5pi/6
-2sqrt3 +2i
given sinx=-3/5 and x is in quadrant 3, what is the value of tanx/2
-3
which expression is a cube root of -1+isqrt 3
3sqrt2 (cos(40 degrees) + isin(40 degrees))
Solve on the interval [0,2pi) 4 csc x+1=-3
3π/2
write the product in standard form: (2-3i)(2+i)
7 - 4i
If the point P(-4/5,y) lies on the unit circle and P is in the third quadrant, what does y equal? If necessary, use the slash mark ( / ) for a fraction bar.
-3/5
evaluate the dot product of (8,4) and (-3,5)
-4
convert the polar representation of this complex number into its standard form: 8(cos(4pi/3)+isin(4pi/3))
-4-4sqrt3i
convert the polar representation of this complex number into its standard form: z=8(cos240 degrees+isin240 degrees)
-4-4sqrt3i
evaluate tan(sin^-1(-5/13))
-5/12
for the function y=-3+4cos((5π)/6(x+4)) what is the minimum value
-7
If tanx=-4/3 and x is in quadrant 2 then cos2x=? A. 7/25 b. -3/5 c. -7/25 d. 3/5
-7/25
which of the following are solutions to the equation: 2cos^2x-1=0
-7pi/4,3pi/4,15pi/4
evaluate tan(cos^-1(-15/17))
-8/15
evaluate tan^-1(-1).
-pi/4
which of the following are solutions to the equation tan^2(2x)-1=0
-pi/8 3pi/8
cos^2xcscx-cscx=___x
-sin
find the exact value of cos(7pi/8)
-sqrt(2+sqrt2)/2
cos ((3\pi )/(4))
-sqrt2/2
find the exact value of cos(11pi/8)
-√(2-√2/4)
if cot=3/4 and the terminal point determined by is in quadrant 3, then
cos==3/5 tan=4/3
The legs of a right triangle measuring 5 inches and 7 units. If theta is the angle between the 5-inch leg and the hypotenuse, cos theta =
.58
cos2x=
cos^2x−sin^2x 1−2sin^2x
to solve the equation 5sin(2x)=3cosx, you should rewrite it as
cosx(10sinx - 3) = 0
Which of the following could be points on the unit circle?
((6)/(7))^(2)+((\sqrt(13))/(7))^(2)=1 ((5)/(13))^(2)+((12)/(13))^(2)=1
evaluate the following expression: 3(1,-1)-(4,-2)
(-1,-1)
Find the terminal point determined by t= 10pi/3
(-1/2, -sqrt.3/2)
convert 4(cos(240 degrees) +isin 240 degrees)) into rectangular form
(-2,-2sqrt3)
Which set of rectangular coordinates describes the same location as the polar coordinates (-2 2pi)
(-2,0)
Which set of rectangular coordinates describes the same location as the polar coordinates 3sqrt2 5pi/4
(-3,3)
convert the polar representation of this complex number into its regular form: z=5(cospi+isinpi)
(-5,0)
use the squared identities to simplify 2sin^2x cos^2x
(1 - cos(4x))/4
which graph appears to show a sinusoid
(1 and 2 only)
Which of the following vectors are orthogonal to (1,5)? Check all that apply A. (-2,5) B. (10,-2) C. (-1,-5) D. (-5,1)
(10,-2) (-5,1)
evaluate the following expression: 2(1,1) - 4 (0,1)
(2,-2) if you dont put the parentheses u get the answer wrong, i hate apex
what is the sum of the two vectors (-1, -4) and (3,5)
(2,1)
Which set of polar coordinates describes the same location as the rectangular coordinates (-5 0)
(5, 180 degrees)
which set of polar coordinates names the same point as (-5,pi/4)
(5, 5π/4)
convert (5,pi/4) to rectangular coordinates
(5√2/2,5√2/2)
Use de moivre's theorem to write the complex number in trigonometric form (cos(2pi/7)+isin(2pi/7))^5
(cos(10pi/7)+isin(10pi/7))^5
Use de moivre's theorem to write the complex number in trigonometric form (cos(3pi/5)+isin(3pi/5))^3
(cos(9pi/5)+isin(9pi/5))
evaluate arccsc2
(pi/6+-2pin,5pi/6+-2pin)
How many solutions does a triangle with side lengths a = 4, A = 68 , and b = 10 have?
0
How many solutions does a triangle with side lengths a=22, A=117 degrees, and b=25 have? Write your answer in numeric form
0
cot ((25\pi )/(2))
0
evaluate sin(Tan^-10)
0
Solve on the interval (0, 2pi): 3 sec x - 2 = 1
0 2pi
Check all that apply. cotθ is undefined for θ = _____. A. 3π/2 B. π/2 C. 0 D. π
0 π
what is the best approximation of the projection of (2,6) onto (5,-1)
0.15(5,-1)
Use the law of cosines to find the value of cos. Round the answer to two decimal places
0.21
Calculate cos theta to two decimal places A. 0.61 B. 1.44 C. 0.72 D. 0.43
0.72
A 50-foot tree casts a shadow 9 feet long. The sine of the angle of elevation..
0.98
For the simple harmonic motion equation d=5sin (2pit), what is the period
1
What value in the nth root of unity for any value n?
1
what is the maximum value that the graph of y=cosx assumes
1
which functions graph has asymptotes located at the values x=+-npi
1 and 4 only
74 degrees is the same as ____ radians
1.29
What is the projection of (4,4) onto (3,1)?
1.6(3,1)
A surveyor measures the angle of elevation to a point on a mountain to be 15 degrees. The point on the mountain is horizontally 6 miles away from the surveyor. The vertical change in elevation from the point where the surveyor is standing to the point on the mountain is ____ miles. (Round your answer to the nearest hundredth of a mile.)
1.61 miles
If the arc length shown in blue is 21.3 inches, then theta to the nearest hundredth of a radian is?
1.78
the equation sin (pi/6 - X) is equal to
1/2(cosx-√3sinx)
For the simple harmonic motion equation d=9cos((π/2)t) what is the frequency? If necessary, use the slash (/) to denote a fraction.
1/4
For the simple harmonic motion equation d=5 sin (pi/4 t), what is the frequency
1/8
The arc corresponding to a central angle of 65 in a circle of radius 10 feet measures _____ feet. Round your answer to two decimal places.
11.34
Find the product of the complex numbers. Express your answer in trigonometric form: z1 = 7(cos15° + isin15°) z2 = 2(cos110° + isin110°)
14(cos125° + isin125°)
Find the product of the complex numbers. Express your answer in trigonometric form: z1 = 7(cos15° + isin15°) z2 = 2(cos110° + isin110°)
14(cos125° + isin125°)
Consider the right triangle given below. The length of side b to two decimal places is ____ (angles, 25 35)
14.34
In a circle of radius 25 inches, a central angle of 35° will intersect the circle forming an arc of length?
15.27 inches
The light from a lamp casts shadow of a man standing 10 feet away from the lamppost. The shadow is 5 feet long. The angle of elevation from the tip of the shadow to the lamp is 50 degrees. How tall is the lamppost, to the nearest foot?
18 feet
A skyscraper casts a shadow 200 feet long. If the angle of elevation of the sun is 49 , then the height of the skyscraper is _____.
180.08 feet
The angle of elevation to the top of a 20-story skyscraper is measured to be 2 degrees from a point on the ground 5,280 feet from the building. What is the height of the skyscraper to the nearest hundredth foot?
184.38
let h=Vo^2/4.9 sin(theta)cos(theta) model the horizontal distance in meters traveled by a projectile. If the initial velocity is 44 meters/second, which equation would you use to find the angle needed to travel 150 meters? A. 395.10sin(2theta)=150 B. 8.98sin(2theta)=150 C. 150sin(2theta)=150 D, 197.55sin(2theta)=150
197.55sin(2theta)=150
For the simple harmonic motion equation d=2 sin (pi/3 t), what is the maximum displacement from the equilibrium position
2
Let the function f(x) have the form f(x) = Acos(x + C). To produce a graph that matches the one shown below, what must the value of C be?. A.1. B.3. C.4. D.2
2
what is the period of the function y=2sinx
2 radian
sin2x=
2 sin x cos x
what is the length of the vector (-4 2)
2 sqrt 5
find the exact value of sin(cos^-1(3/7))
2 sqrt10/7
What is the horizontal displacement of the basic graph to produce a graph of y=pi-3cos(x-2)
2 units right
the exact value of tan(5pi )/(12)
2+√3
the radian measure of an angle that is 125 degrees 25'50''
2.19
A dog that has been tethered with a _____foot lead makes the path shown here. The length of the path is 45 feet, and the measure of the angle is 2.25 radians.
20
find the product of the complex numbers. express ur answer in trigonometric form z1 = 3(cos(π/4) + isin(π/4)) z2 = 7(cos(3π/8) + isin(3π/8))
21(cos(5π/8) + isin(5π/8))
Calculate the length b to two decimal places
21.64
4 radians is the same as
229.18
Dr. Black is standing 13 feet from the streetlamp. The lamp is making his shadow 9 feet long. He estimates that the angle of elevation from the tip of his shadow to the top of the streetlamp is 50 degrees. To the nearest foot, the streetlamp is about _______
26
1+cos(12x)
2cos^2(6x)
what is the period of the secant function
2pi
which of the following are solutions to (2tanx)/(1-tan^2x)=sqrt3
2pi/3 + npi , pi/6 + npi
Solve on the interval (0, 2pi): 2 sec x + 5 = 1
2pi/3,4pi/3
1-cos(6x)=
2sin^2(3x)
which complex number's graph is shown below (point at 2, -2)
2sqrt(2)(cos(7pi )/(4)+isin(7pi )/(4))
evaluate the dot product of (-1,2) and (-3,3)
3
Which of the following is a third root of the given complex number? 27(cos(pi/5)+isin(pi/5))
3(cos(pi/15)+i sin(pi/15)) 3(cos(11pi/15)+i sin(11pi/15))
If v1=(2,5) and v2=(4,-3), then the angle between the two vectors is____degrees. Round your answer to two decimal places
31.33
42.54deg is the same as 42deg___'24''
32
What is the equivalent value of "32 degrees 15' 66"? Round to the nearest hundredth of a degree.
32.27
In the triangle below, b=___. If necessary, round your answer to two decimal places.
35.00
The law of cosines is a2+b2 - 2abcosC = c^2 find the value of 2abcosC .... A. 40 B. -40 C. 37 D. 20 (The sides are 2,4, and 5; A to B is 2, B to C is 4, and A to C is 5.)
37
which value is a solution for the equation cot x/2=-1
3pi/2
Which of the following are solutions to the equation sinx cos(pi/7)-sin(pi/7)cosx=sqrt(2)/2 check all that apply A. 7pi/4+pi/4+2npi B. 5pi/4+pi/7+2npi C. pi/4+pi/7+2npi D. 3pi/4+pi/7+2npi
3pi/4+pi/7+2npi pi/4+pi/7+2npi
which expression is a cube root of -2i
3sqrt2 (cos(210 degrees)+isin(210 degrees))
Fill in the blank. In the triangle below, x = ______. Round your answer to two decimal places
44.80
Suppose an isosceles triangle ABC has A=pi/4 and b=c=4. What is the length of a^2?
4^2(2-sqrt(2)
For the simple harmonic motion equation d= 5sin((pi/4)t)n , what is the maximum displacement from the equilibrium position
5
What is the minimum number of points required to mark all maximum, minimum, and zeros in a period of a sinusoid
5
calculate: |-3+4i|
5
for the function y=-1+6cos((2π)/7(x-5)) what is the maximum value
5
what is the amplitude of the sinusoid given by y=-5sin(7x)
5
what is the period of the sinusoid given by y=-3cos(2π/5(x))
5
Which of the following are solutions to the equation sinx cosx = 1/4? Check all that apply. A. 5(pi)/12 +n(pi) B. pi/3 + n(pi)/2 C.pi/12 + n(pi) D. pi/6 + n(pi)/2
5(pi)/12 +n(pi) pi/12 + n(pi)
Find the quotient of the complex numbers. Express your answer in trigonometric form. z1= 5(cos25Deg + i sin25Deg) z2= 2(cos80Deg + isin80Deg)
5/2(cos305Deg-i sin305Deg)
if sin=-4/5 and theta is in qaudrant 4, the value of sec theta is
5/3
In the triangle below, b = _____. If necessary, round your answer to two decimal places (42 degrees, 41.5)
54.94
rewrite the square root expression as an imaginary number: sqrt -25
5i
A complex number will in general have ____ sixth complex roots
6
simplify: (4-3i)+(2+6i)
6+3i
What is the reference angle for 295 degrees?
65
Suppose a triangle has two sides of length 42 and 35, and that the angle between these two sides is 120. What is the length of the third side of the triangle
66.78
find the conjugate of the complex number: 7-3i
7+3i
Swanson plans to attempt to swim across the lake from point A to point B as shown below. To determine how far he will have to swim, he has chosen a point C and determined the labeled distances. How many miles will he have to swim? Round your answer to two decimal places
70.40
For the simple harmonic motion equation d=5sin (pi/4 t), what is the period
8
How many solutions does the equation sin(4x)=1/2 have on the interval (0 2pi)
8
Use de moivre's theorem to write the complex number in trigonometric form: (1-isqrt3)^3
8(cospi+isinpi)
simplify: (-2+3i)+2(5+6i)
8+15i
simplify: (5+2i)-(-3+4i)
8-2i
if sin theta > 0 and tan theta < 0 then
90 degrees < theta < 180 degrees
Which of the following triangles are right triangles? Check all that apply. A triangle with side lengths 5, 12, 13 A triangle with side lengths 6 inches, 8 inches, 10 inches A triangle with side lengths 8, 15, 17 A triangle with side lengths 9, 12, 16
A triangle with side lengths 5, 12, 13 A triangle with side lengths 8, 15, 17 A triangle with side lengths 9, 12, 15
(___)^2=(cscx-1)(cscx+1) ?
cotx
An arc of length 10 meters is formed by a central angle A on a circle of radius 4. The measure of A in degrees (to two decimal places) is _____. A. 143.24 B. 2.50 C. 216.76 D. 36.76
A. 143.24
An angle measuring 5.25 radians is equal to which of the angle measures given below? Check all that apply.
A. 300 degrees 48' 10" B. 300.80 degrees
refer to the figure below and mark all statements that are true
A. If the ratio of the arc length to r is 1, then the measure of is 1 radian.
Which of the following problem types can always be solved using the law of cosines or sines? Check all that apply
A. SSS C. ASA D. SAA F. SAS
Suppose a triangle has sides a, b, and c, and that a^2 + b^2 < c^2. Let be the measure of the angle opposite the side of length c. Which of the following must be true?
A. cosθ < 0 C. the triangle is not a right triangle D. θ is an obtuse angle
Which of the following are correct statements concerning the roots of unity? Check all that apply. A. nth roots of unity are evenly spaced on the unit circle. B. 1 is always the nth root of unity. C. The number of nth roots of unity is n. D. -1 is always the nth root of unity.
A. nth roots of unity are evenly spaced on the unit circle. B. 1 is always the nth root of unity. C. The number of nth roots of unity is n.
Which of the functions have a range of all real numbers greater than or equal to 1 or less than or equal to -1? check all that apply. A. y=sec x B. y= tan x C. y= cot x D. y= csc x
A. y=sec x D. y= csc x
Mark the statements that are true A. An angle that measures 2.5 radians is an acute angle. B. An angle that measures 3.5 radians is an obtuse angle. C. An acute angle measures less than 90. D. An angle that measures 285 is a reflex angle.
An acute angle measures less than 90°. An angle that measures 285° is a reflex angle.
In the following triangle, theta= 60. find the values of the angles B and B', which solve this ambiguous case
B = 66.25 degree or B' = 113.75 degree
What is true about the complex number -5 - 5i? Check all that apply. A. The modulus is 10. B. It lies in quadrant 4. C. It lies in quadrant 2. D. The modulus is 5 square root of 2.
B. The modulus is 5sqrt2 C. It lies in quadrant 4
Which of following equations are identities. Check all that apply. A. sec x = 1/csc x B. csc x = 1/sin x C. tan x = cos x/sin x D. cot x = 1/tan x
csc x = 1/sin x tanx = sinx/cosx
the function f(x)=cot(3x-pi/2) has
Period: pi/3 asymptote: x=pi/6
What does the law of cosines reduce to when dealing with a right triangle? A. The Pythagorean theorem B. The formula for a triangle's area C. The law of sines D. The formula for a triangle's area
Pythagorean theorem
Which of the following problem types can always be solved using the law of sines AAS ASA SAS SSS
SSS AAA SAS
Which features are present in this polar graph? (cardiod on right side of graph)) A.Symmetry about the line theta =pi/2 B.Symmetry about the polar axis theta= 0 C.Symmetry about the pole (0,0) D.No symmetry
Symmetry about the polar axis theta= 0
In order to apply the law of cosines to find the measure of an interior angle, it is enough to know...?. . A. The lengths of all three sides of the triangle.. B. The area of the triangle. C. At least two of the angles of the triangle and the length of one of its sides
The lengths of all three sides of the triangle
Let v = (2,8) and w = (-1,-4). Which of the following is true? Check all that apply.
The x-component of v is 2. v+w=-34 v=-2w
Which of the following would be an acceptable first step in simplifying the expression cosx / 1-sinx ?
[ cos(x) * (1 + sin(x)) ] / [(1-sin(x) * (1+sin(x)]
In this triangle, which of the following is true?
a. The measure of x is 55° and a ≈ 11.47
Calculate the side lengths a and b to two decimal places
a= 15.09 b = 15.81
Calculate the side lengths a and b to two decimal places
a=11.71, b=15.56
assume the graph of a function of the form y=acos(k(x-b)) is given below. which of the following are possible values for a,k,b
a=4, k=2,b=-pi/4
Suppose a triangle has sides a, b, and c, and let theta be the angle opposite the side length of b. if costheta > 0, what must be true?
a^2 +c^2 > b^2
Suppose a triangle has sides a, b, and c, and the angle opposite the side of length b is obtuse. What must be true? A. a2 + c2 < b2 B. a2 + c2 > b2 C. b2 + c2 < a2 D. a2 + b2 < c2
a^2+c^2<b^2
the domain of the sine function is ___
all real numbers
the function f(x)=-2cos(3x-(pi )/(4)) has
amplitude 2 and period 2pi/3
The displacement of a mass suspended on a spring is modeled by the function y = 3sin(4)(pi)(t), where y is measured in inches and t in seconds. The amplitude, period, and frequency of the motion of the mass are given by
amplitude=2 period=2/3 frequency=3/2
Mark the statements that are true an angle that measures 180 also measures pi radians An angle that measures π/6 radians also measures 30° An angle that measures π/3 radians also measures 45° an angle that measures 30 also measures pi/3
an angle that measures 180 also measures pi radians An angle that measures π/6 radians also measures 30°
The vertical _____ of the function cosecant are determined by the points that are not in the domain.
asymptote
Which of the following pairs of coordinates do not represent the same point in polar coordinates? Choose all that apply a. (r , theta) and (r , theta+2pi) b. (r , theta) and (-r , theta+2pi) c. (r , theta) and (-r , theta) d. (r , theta) and (-r , theta+pi)
b. (r , theta) and (-r , theta+2pi) c. (r , theta) and (-r , theta)
In the following triangle, find the values of the angles B and B', which are the best approximations to the solutions of this ambiguous case
b=59.6 or b=120.4
If triangle ABC has angle 52 side a=200 and side b=234 then which of the following is true
b=67.2 or 112.8
The statement "cot theta= 12/5, sec theta = -13/5, and the terminal point determined by theta in quadrant 4"
cannot be true because secant theta is greater than zero in quadrant 4.
what is the name of the shape graphed by the function r=1+sintheta
cardiod
what is the name of the shape graphed by the function r=3+3costheta
cardiod
what is the name of the shape graphed by the function r=1+sin theta
cardioid
what is the name of the shape graphed by the function r=4sin theta
circle
sin pi/4 sin pi/6 = 1/2(___ pi/12 - cos 5pi/12)
cos
if sin=2/3 which of the following are possible
cos(-)= sqrt.5 / 3 and tan(-)= 2/ sqrt.5 sec (-) 3/sqrt5 and tan(-)= 2/ sqrt.5
the expression cosx(cosx-tanxsinx) simplifies to
cos(2x)
Suppose a triangle has sides a, b, and c with side c the longest side, and that a2 + b2 > c2. Let θ be the measure of the angle opposite the side of length c. Which of the following must be true
cos(θ)>0 is true angle θ is acute
Check all that apply. If sec=13/12, then:
cos=12/13 tan=5/12