unit 9 precalc apex
find the exact value of cos(11pi/8)
-√(2-√2/4)
How many solutions does a triangle with side lengths a = 4, A = 68 , and b = 10 have?
0
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)
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
How many solutions does the equation sin(4x)=1/2 have on the interval (0 2pi)
8
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
Calculate the side lengths a and b to two decimal places
a= 15.09 b = 15.81
cos2x=
cos^2x−sin^2x 1−2sin^2x
A vector has both a direction and a ____. A. Reverse B.Scalar C. Zero D. Magnitude
magnitude
_____ pi/3 cos pi/6 = 1/2 (sin pi/2 + sin pi/6)
sin
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
the exact value of cos(17pi )/(8)
√(2+√2)/4
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)
The equation tan(x+pi/3) is equal to?
(√3 tanx+1)/(√3-tanx)
given sinx=-3/5 and x is in quadrant 3, what is the value of tanx/2
-3
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
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
In the triangle below, b = _____. If necessary, round your answer to two decimal places (42 degrees, 41.5)
54.94
Which of the following problem types can always be solved using the law of sines AAS ASA SAS SSS
SSS AAA SAS
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
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
the expression cosx(cosx-tanxsinx) simplifies to
cos(2x)
A vector has both a direction and a ____. A. Reverse B.Scalar C. Zero D. Magnitude
magnitude
___ cosb=1/2(sin(a+b)+sin(a-b)
sin a
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
If the dot product of two nonzero vectors v1 and v2 is nonzero, what does this tell us
they are not perpendicular
use the squared identities to simplify 2sin^2x cos^2x
(1 - cos(4x))/4
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
evaluate the dot product of (8,4) and (-3,5)
-4
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
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
(True or False) All equations are identities, but not all identities are equations.
false
(true or false) cos(x/5)sin(x/5)=1/2(sin(2x/5))
true
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
which of the following are solutions to (2tanx)/(1-tan^2x)=sqrt3
2pi/3 + npi , pi/6 + npi
1-cos(6x)=
2sin^2(3x)
evaluate the dot product of (-1,2) and (-3,3)
3
In the triangle below, b=___. If necessary, round your answer to two decimal places.
35.00
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
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 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
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
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)]
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
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
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
to solve the equation 5sin(2x)=3cosx, you should rewrite it as
cosx(10sinx - 3) = 0
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
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
(true or false) SSA triangle problems will have either one or two solutions
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) all trigonometric equations are identities
false
(true or false) tan^2x=(1+cos2x)/(1-cos2x)
false
(true or false) the equation cosx=sqrt3/2 is an identity
false
The expression (tanx + cotx)^2 is the same as ___
sec^2x + csc ^2 x
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
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)
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
(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
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
(true or false) Sin(a-b) = sinacosb+cosasinb for all values of a and b
false
(true or false) Cos2a=1-2sin^2a for all values of a.
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
evaluate the following expression: 3(1,-1)-(4,-2)
(-1,-1)
what is the sum of the two vectors (-1, -4) and (3,5)
(2,1)
cos^2xcscx-cscx=___x
-sin
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
Calculate the side lengths a and b to two decimal places
a=11.71, b=15.56
(csc(4x)-cot(4x))/(csc(4x)+cot(4x))
tan^2(2x)
(true or false) sin(-x)=-sin x for all values of x
true
evaluate the following expression 4(3,5)-2(7,-2)
-2,24
the equation sin (pi/6 - X) is equal to
1/2(cosx-√3sinx)
sin pi/4 sin pi/6 = 1/2(___ pi/12 - cos 5pi/12)
cos
(___)^2=(cscx-1)(cscx+1) ?
cotx
(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
A. sin2x - cos2x = 1 B. tan2x = sec2x - 1 C. sin2x = 1 - cos2x D. cot2x + csc2x = 1
tan2x = sec2x - 1 sin2x = 1 - cos2x
(true or false) sin(75 degrees)=sqrt(1-cos(150 degrees)/2)
true
(true or false) The law of cosines can only be applied to right triangles
false
The expression sinx(cscx - cotx cosx) can be simplified to:
sin² x
(true or false) Cos(a/2) = ± √(1 - cosa)/2 for all values of a
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) sec(pi/2-x)=cscx
true
(true or false) triangulation is a method of finding the location of an object based on measurements made from two other locations
true
What is the projection of (4,4) onto (3,1)?
1.6(3,1)
sin2x=
2 sin x cos x
what is the length of the vector (-4 2)
2 sqrt 5
the exact value of tan(5pi )/(12)
2+√3
Calculate the length b to two decimal places
21.64
1+cos(12x)
2cos^2(6x)
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)
