Math Trig
What is tan (x+P)?
tan x
What is tan (x+π)?
tan x
What is the domain of cosx?
(-∞, ∞)
What is secant on the unit circle?
1/x
Evaluate sec π/3
2
What is the period of secant?
2π
What is the period of sine?
2π
If we know sec = 13/5, find the other trig
cos - 5/13 sin - 12/13 tan - 12/5 csc- 13/12 cot - 5/12
What are the coordinates of 240?
(-1/2, -√3/2)
What point has the same trig values as (-5,12)?
(-10, 24)
What is the coordinates of 0 and 360 degrees?
(1,0)
What is cosecant on the unit circle?
1/y
Convert from decimal for to DMS: 118.32o
118o 19' 12"
What are the coordinates of 120 degrees?
(-1/2, √3/2)
What are the coordinates of 225?
(-√2/2 , -√2/2)
What are the coordinates of 135?
(-√2/2 , √2/2)
What is the point on the terminal side of 7π/6 degrees?
(-√3, -1)
What are the coordinates of 210?
(-√3/2, -1/2)
What are the coordinates of 150?
(-√3/2, 1/2)
What are the coordinates of 330?
(-√3/2, 1/2)
What is the domain of sinx?
(-∞, ∞)
What are the coordinates of 270?
(0,-1)
What is the coordinates of 90 degrees?
(0,1)
What are the coordinates of 300?
(1/2, -√3/2)
What is the coordinates of 60 degrees?
(1/2, √3/2)
What is the point on the terminal side of 45 degrees?
(2,2)
What is (x,y) in sin + cos?
(cos O, sin O)
What are the point of inflection?
(nπ, 0)
What are the coordinates of 315?
(√2/2 , -√2/2)
What is the coordinates of 45 degrees?
(√2/2 , √2/2)
What is the coordinates of 30 degrees?
(√3/2, 1/2)
Determine the sign of cos 7π/8
-
What happens in 5sinx?
-1 and 1 become -5 + 5
If a non horizontal line has a slope sin theta, it will be perpendicular to a line with what slope?
-csc theta
What is e^x * sinx greater than and less than?
-e^x < e^x * sinx < e^x
What is the derivative of cos(x^2+1)?
-sin (x^2+1) * 2x = -2x * sin (x^2 + 1)
Evaluate sin 11π/3
-√3 / 2
What is the cos of (-7π/6)?
-√3/2
Use calculator to calculate: tan (π/12)
.268
Use calculator to calculate: cot 0.89
.810
Use calculator to calculate: cos 19o23'
.943
At the initial with no rotation, what is the degrees?
0
Evaluate by using the period of the function: cos (5,555,555π/2)
0
A weight suspended from a spring is set into motion. Its displacement d from equilibrium is modelled by d = 0.4e^-0.2t cos 4t. Evaluate for t =0 and t=3
0 = 0.4 3 = .1852
What is the tangent of (4,0)?
0/4
Evaluate tan -15π/4
1
What Quadrant is an acute angle in?
1
What is tan (pi / 4)?
1
What is the hypotenuse of 45-45-90 triangle?
1
What is the hypotenuse of the 30-60-90 triangle?
1
What is tan (pi / 6)?
1 / root 3
Convert from DMS to radians: 61o 24'
1.0716 radians
Evaluate by using the period of the function: sin (π/6 + 49,000π)
1/2
What is cos (pi / 3)?
1/2
What is sin (pi / 6)?
1/2
What is the shortest leg of the 30-60-90 triangle?
1/2
What is one regrees in terms of revolutions?
1/360
What is one second in degrees?
1/3600
What is one second in minutes?
1/60
What is one minute in terms of degree?
1/60th
Find the cosine given the cosecant = 5
1/y = 5 cosine = r/y r = 5 and y = 1 cos = 2 root 5 / 5 1^2 + x^2 = 25 x = + or - 24
What are bearings?
100 degrees off the north......clockwise
Convert from radians to degrees: 2
114.59 o
What are the radians of 330?
11π / 6
A radial arm saw has a circular cutting blade with a diameter of 10 inches. It spins at 2000 rpm. If there are 12 cutting teeth per inch on the cutting blade, How many teeth cross the cutting surface each second?
12,566.37
A bike w 26 in diameter wheels is traveling at 10 mph. To the nearest whole number, how many revolutions does each wheel make per minute?
129
What is r for (-5,12)?
13
If the short leg is 15 and the opposite angle is 34, what is the length of the hypotenuse?
15 / sin 34 = 26.82
A simple pulley with radius 4 is used to lift heavy objects is positioned 10 feet above ground level. Given that the pulley rotates 720 degrees, determine the height to which the object is lifted.
16 pi
What degree is pi equal to?
180
Convert from radians to degrees: π/10
18o
What Quadrant is an obtuse angle in?
2
csc (π/3)
2 / √3
What is one revolution in radians?
2 pi
If sin o = 0.4, then sin (-o) + csc (o) =
2.1
A guy wire from the top of the transmission tower forms a 75 degree angle with the ground at a 55 foot distance from the base of the tower. How tall is the tower?
205.26 feet
Convert from DMS to decimal form: 118o 44' 15"
23.2o
To the nearest inch, find the perimeter of a 10-degree sector cut from a circular disc of radius 11 inches.
24 inches
The belt on a car air conditioner connects metal wheels with r= 4 cm and R = 7 cm. The angular speed of the larger wheel is 120 rpm. What is the linear speed of the belt in cm per second?
28 pi cm/sec
What is the period of cosecant?
2π
What is the period of cosine?
2π
What is the radians of 0 and 360 degrees?
2π
What is the radians of 120 degrees?
2π / 3
Convert from DMS to radians: 120o
2π/3
Use the appropriate arc length formula to find the missing info: s - 3, r = 1 and ø = ?
3 radians
What is 8 Σ (2x+1) ? k=1
3+5+7+.........+17
What are the four pythagorean triples?
3-4-5 5-12-13 7-24-25 8-15-17
If sin = 1/2 what is the reference angle?
30
What an angle has radians over 6, what is the reference angle?
30
Find the acute angle that satisfies the given equation (in both radians and degrees): tan O = √3 / 3
30 degrees π/6
If the long leg is 32 and its opposite angle is 57, what is the short leg?
32 / tan 57 = 20.78
What is one revolution is degrees?
360 degree
Use the appropriate arc length formula to find the missing info: s - 40, r = ? and ø = 18o
360/π
Mary's team of surveyor had to find the distance AC across the lake at a park. Field assistants positioned themselves at points A and C while mary sets up an angle measuring instrument at point B, 100 feet from C in a perpendicular direction. Mary measured angle ABC as 75o12'42". What is the distance AC?
378.80
A girl races on a bicycle with 13 in radius wheels. When she is traveling at a speed of 44 ft/sec, how many revolutions per minute are her wheels making?
387.85 rpm
What is the derivative of 3sinx?
3cosx
What are the radians of 270?
3π / 2
What are the radians of 135?
3π / 4
The belt on a car air conditioner connects metal wheels with r= 4 cm and R = 7 cm. The angular speed of the larger wheel is 120 rpm. What is the angular speed of the larger wheel in radians per second?
4 pi radians per second
Two coast guard patrol boats leave Cape May at the same time. One travels with a bearing of 42o30' and the other with a bearing of 52o12'. If they travel at the same speed, approximately how far will they be when they are 25 statute miles from Cape May?
4.23 statute miles
What is the cosine of (4,0)?
4/4
What is the secant of (4,0)?
4/4
Change 43.18 to DMS
43 .18 x 60 = 10.8 .8 x 60 = 48 43 - 10.8 minutes - 48 seconds
If cos = root 2 / 2, what is the reference angle?
45
If cot = 1, what is the reference angle?
45
What an angle has radians over 4, what is the reference angle?
45
What are the two special triangles?
45-45-90 30-60-90
What is angle is not coterminal with the others: 150, 510, -210, 450, 870?
450
What is the radians of 240?
4π / 3
It takes 10 identical pieces to form a circular track for a pair of toy racing cars. If the inside arc of each piece is 3.4 inches shorter than the outside arc, what is the width of the track?
5.4 inches
What are the radians of 300?
5π / 3
What are the radians of 225?
5π / 4
What is the radians of 150?
5π / 6
Use the appropriate arc length formula to find the missing info: s - 1.5, r = ? and ø = π/4 radians
6 / π
If cot = 1/root 3, what is the reference angle?
60
What an angle has radians over 3, what is the reference angle?
60
Find the acute angle that satisfies the given equation (in both radians and degrees): sec O = 2
60 degrees π/3
The belt on a car air conditioner connects metal wheels with r= 4 cm and R = 7 cm. The angular speed of the larger wheel is 120 rpm. What is the angular speed of the smaller wheel in radians per second?
7 pi rad/sec
Points C and D are 895 statute miles apart. How far are C and D in nautical miles if one statute mile is .87 nautical miles?
778
What are the radians of 315?
7π / 4
What is the radians of 210?
7π / 6
Change 8 degrees 11' and 20 " to decimal degree
8 11 / 60 20 / 3600 8.19
When the Taylor Polynomial is a=0, what is it called?
A Maclaurin Series
What is the unit circle?
A circle with center (0,0) and a radius one
What do x and y describe?
A circle with center (0,0) and radius r
What is a periodic function?
A function that for some interval of the domain, it's range repeats
What is an oscillating function?
A function that is DNE on both sides
What is a reference angle?
A positive acute angle between the terminal side and the x axis
In the coterminal angle form, what does n equal?
A set in Z
In the coterminal angle form, what does z equal?
A set of integers
What is cosine?
Adjacent / Hypotenuse
What is cotangent?
Adjacent / Opposite
What can x and y be?
All real numbers
What is cosecant?
Hypotenuse / Opposite
When is an angle at standard position?
If 1. vertex is at origin 2. Initial side as positive x-axis
When is a function anti periodic?
If f(x+P) = -f(x)
What can any point in the plane except the origin be defined by?
In terms of ø, x, y, and r
What are examples of well defined?
Linear sets of real nunbers
Extrema of cosx?
Max (2nπ, 0) Min ((2n+1) π, 0)
How do you graph the unit circle on calc?
Mode - Parametric X1 = cos (T) Y1 = sin (T) Window (-2,2) (-2,2) Zoom Square
What is periodicity?
Multiples of degrees and pi
How do you convert radians to degrees?
Multiply by 180 / π radians
How do you convert degrees to radians?
Multiply by π radians / 180
What are the VA and HA of cosx?
None
What is the H and V asymptote of sinx?
None
In Taylor Series, what does n stand for?
Number of series
What is tangent?
Opposite / Adjacent
What is sin?
Opposite / Hypotenuse
What happens when the anti period is doubled?
Period
What happens in sinx/5?
Period becomes 10π
What is r always?
Positive
What does r equal?
Radius
Extreme of sinx?
Relative Max - (π/2 + 2nπ) Relative Min - (-π/2 * 2nπ)
What is sin (pi / 4)?
Root 2 / 2
What is tan (pi / 3)?
Root 3
What is sin (pi / 3)?
Root 3 / 2
What is the equation for arc length?
S = rø
What quadrant is (-5,12) in?
Second
Short leg - 5 Long leg - 12 Hypotenuse - 13 Find all six trig functions
Sin - 12/13 Cos - 5/13 Tan - 12/5 Csc - 13/12 Sec - 13/5 Cot - 5/12
What is a period?
The smallest interval for which the function repeats
What is the formula for r?
The square root of the sum of x squared and y squared
What determines the quadrant or axis of angle?
The terminal side
What is the formula for Taylor Polynomials?
Tn (x) = n Σ f(t) (a)/t! (x-a)^t t=0
What did L'Hospital discover?
When indeterminate, take the derivative of numerator and denominator
What is the continuity of cos x?
Yes, over D
What is the continuity of sinx?
Yes, over its domain
What is the range of cosx?
[-1, 1]
What is the range of sinx?
[-1, 1]
In the unit circle, what is x?
cos (T)
Concavity of cosx?
f"(x) = -cosx Up (π/2, 3π/2) (-3π/2, -π/2) Down (-π/2, π/2)
What is the concavity of sinx?
f"(x) = -sinx Up - (-2π, π) (0, π) Down - (-π, 0) (π, 2π)
What is the inc/dec of cosx?
f'(x) = -sinx nπ Increasing (-π,0) (π, 2π) Decreasing (-2π, -π) (0,π)
What is the inc/dec for sinx?
f'(x) = cosx Increasing - (-5π/2, -3π/2) (-π/2, π/2) (3π/2, 5π/2 Decreasing - (-3π/2, -π/2) (π/2, 3π/2)
What is the end behavior of sinx?
lim sinx = DNE x -> ∞ lim sinx = DNE x -> -∞
What is the end behavior of cosx?
lim sinx = DNE x -> ∞ lim sinx = DNE x -> ∞
In Taylor Series, what is the upper bound?
n
What is the radian measure of an angle of x degrees?
pi x / 189
What are the two shorter sides of a 45-45-90 triangle?
root 2 / 2
What is cos (pi / 6)?
root 3 / 2
What is the longer leg of the 30-60-90 triangle?
root 3 / 2
Use the appropriate arc length formula to find the missing info: s - ?, r = 2 and ø = 25
s = 50
What is the arc length formula for radians ?
s = rø
What is the arc length formula for degrees?
s = πrø / 180
Find sec o and csc o if cot o = -4/3 and cos o<0
sec o = -5/4 csc o = 5/3
In the unit circle, what is y?
sin (T)
What is sin (π/6 + 49,000 π / 2πn + O)?
sin (π/6) = 1/2
Evaluate the six trig functions for (0,5)
sin - 1 cos - 0 tan - undefined csc - 1 sec - undefined cot - 0
If P(-1,2), what are the six trig functions for theta?
sin - 2/√5 cos - -1/√5 tan - -2 csc - √5/2 sec - -√5 cot - -1/2
The index of refraction (u) is found in the equation sin o1 = u sin o2; if o1 =83 and o2 = 36, find the index of refraction?
sin 83 / sin 36 = 1.69
State the sign of sin, cos, and tan for (0, π/2)
sin = + cos = + tan = +
Find sin, cos and tan for the given angle: -450 degrees
sin = -1 cos = 0 tan = Undefined
Find sin, cos and tan for the given angle: -7π/2
sin = -1 cos = 0 tan = Undefined
Find sin o and tan o if cos o = 2/3 and cot o > 0
sin o = √5 / 3 tan o = √5 / 2
What is sin (x+2π)?
sin x
What is sin (x+P)?
sin x
What trig functions have no restrictions?
sine and cosine
What is the lim of sinx/x as x goes to 0?
sinx/x = 1 Derivatives = cosx / 1 = 1/1 = 1
What does cosine equal in terms of x, y and r?
x / r
What does cotangent equal in terms of x, y and r?
x / y
What is the intercepts of cos x?
x = (π/2 + nπ, 0) y = (0,1)
Find the cot given cos = -1
x = -1 r = 1 y = 0 cot = undefined
Find the sine given tan = -3/8
x = -8 y = 3 64+9 = 73 sin = 3/root 73
What is the restriction on secant?
x can't equal 0
What is the restriction on tangent?
x can't equal 0
What is cotangent on the unit circle?
x/y
What is sin on the unit circle?
y
What does sine equal in terms of x, y and r?
y / r
What does tangent equal in terms of x, y and r?
y / x
What is the restriction on cosecant?
y can't equal 0
What is the restriction on cotangent?
y can't equal 0
What is the intercepts of sinx?
y-int : y=0 x-int : x = 0 + 2πr x = π + 2πr
What is tangent on the unit circle?
y/x
What is the range of the function f(t) = (sin t)^2 + (cos t)^2?
{1}
What is the formula for theta of coterminal angles?
Øterminal = Ø + 360n
What do the variables stand for in s = rø?
ø - central angle in a circle r - radius of the circle s = Length of arc
A central angle ø intercepts arcs s1 and s2 on two concentric circles w radii r1 and r2. ø = ?, r1 = 11, s1 = 9, r2 = 44, s2 = ?
ø = 9/11 radians s2 = 36 cm
What is the period of cotangent?
π
What is the period of tangent?
π
What is the radians of 180?
π
What is the radians of 90 degrees?
π / 2
What is the radians of 60 degrees?
π / 3
What is the radians of 45 degrees?
π / 4
What is the radians of 30 degrees?
π / 6
POI of cosx?
π/2 + nπ
What radians have the sin 1/2?
π/6 and 2πn
sec 45 degrees
√2
cos (π/4)
√2 / 2
What is the sin of (3π/4)?
√2/2
What is the tangent of (-π/3)?
√3
sin (π/3)
√3 / 2
What are the coordinates of 180?
(-1,0)
In Taylor Series, what is the lower bound?
t=o
What is the sine of (4,0)?
0/4
What are coterminal angles?
Angles in standard position with the same terminal side
What have the same trig values?
Any point on the same line
What are non periodic functions called?
Aperiodic
What type of math are Taylor polynomials?
Arithmetic
In Taylor Series, what does t=0 stand for?
Derivative
What is well defined?
Each point is mapped to exactly 1 nunber
T or F: If theta is an angle in any triangle, than tangent theta is the length of the side opposite theta divided by the length of the side adjacent to theta.
False
How does affecting x move the unit circle?
Horizontally
What is secant?
Hypotenuse / Adjacent
Assuming that ø is an acute angle in a right triangle, evaluate the remaining trig functions: cos ø = 5/11
Sin - 4√6 / 11 Tan - 4√6 / 5 Csc - 11 / 4√6 Sec - 11 / 5 Cot - 5 / 4√6
Assuming that ø is an acute angle in a right triangle, evaluate the remaining trig functions: csc ø = 23/9
Sin - 9 / 23 Cos - 8√7 / 23 Tan - 9 / 8√7 Sec - 23 / 8√7 Cot - 8√7 / 9
Short leg - 8 Long leg - ? Hypotenuse - 11 Theta at angle between 8 and 11 Find all six trig functions
Sin - Root 57/11 Cos - 8/11 Tan - Root 57/8 Csc - 11/Root 57 Sec - 11/8 Cot - 8/ Root 57
What is parametric?
The Unit Circle
What is 1 radian?
The length of an arc of equal to the radius of the circle it intercepts
In parametric functions, what does T equal?
The parameter
What are 60 and -300 degrees?
The same point
When are sine and cosine anti periodic?
with π
What does secant equal in terms of x, y and r?
r / x
What does cosecant equal in terms of x, y and r?
r / y
What is the Taylor series when a = 0?
Tn (x) = n Σ f(t) (a)/t! (x-a)^t t=0 Tn (x) = n Σ f(0) /0! = 1 t=0 t = 1 ---> n Σ x^t / x! = 1 + x + X^2/2! + X^n/n! t=0 e(1) = 1 + 1 + 1/2 + 1/6 + 1/24 +...........
T or F: If horse A is going twice as far as horse B from the center of a merry go round, then horse A travels twice as fast as horse B.
True
T or F: If o is an angle of a triangle such that cos o < 0, then o is obtuse
True
What is the cosecant of (4,0)?
Undefined
What is the cotangent of (4,0)?
Undefined
How does affecting y move the unit circle?
Vertically
What is the terminal side?
Where the ray stops after rotation
What is cosine on the unit circle?
x
For the point (4,0), what does x, y, and r equal?
x - 4 y - 0 r - 4