Download Trigonometry Review Guide

Trigonometry Review Guide
Sketch each angle and determine the quadrant that contains the angle’s terminal side
1.
2.
110
3.
-60
255
Find the measure of each angle from both the positive and negative perspective
4.
5.
20
40
Counterclockwise (Positive)
Clockwise (Negative)
Counterclockwise (Positive)
Clockwise (Negative)
Use the correct formulas to convert each measure from degrees to radians or vice versa
Degrees
210
Radians
3p
4
-315
108
7p
10
The chart below deals with coterminal angles. If an angle is in degrees, give your answer
in degrees. If an angle is in radians, give your answer in radians
Angle
Reference Angle
Positive Coterminal Angle
Negative Coterminal Angle
560
-380
9p
4
-
17p
7
1020
43p
5
18632
-
76p
3
361
6. Given an angle measuring 1190 , find a coterminal angle between 0 and 360
7. Given an angle measuring
25p
, find a coterminal angle between 0 and 2p
3
Find exact values of sine, cosine, and tan (Hint: Draw triangles)
8.
9.
q = 240
q = 315
sin 240 =
sin315 =
cos240 =
cos315 =
tan240 =
tan315 =
NO CALCULATORS
Find the exact value of each of the following. Remember to think about where the
angle falls on the unit circle and whether you are dealing with x or y.
(HINT: Your answers will be -1, 0, or 1)
10.
sin180
11. cos180
12. sin
p
2
13. cos 90
State whether each expression is positive or negative
14.
cos155
15. sin 235
16.
sin181
17.
cos 45
18.
cos- 89
19. tan 210
20.
tan 280
21.
sin
Identify the quadrant being described
22.
sin q < 0
cos q < 0
23.
cos q > 0
tan q < 0
7p
8
Complete each statement with <, >, or =
24.
sin 90
sin 95
25.
cos 80
cos 40
26.
sin100
sin 80
27.
cos115
cos170
28.
tan175
tan 40
29.
cos- 45
cos- 135
Find the arc length and area of the sector
30.
31.
10 in
5p
3
32.
The central angle of a sector is
of the sector is 6p in2 ?
p
3
r = 6 in
2p
q=
5
radians. What is the measure of the radius if the area
Answer each question by using the general equation of the sine and cosine function
33.
y = 4cos5(x- 2)
What is the min and max point?
What is the amplitude?
How many cycles occur from 0- 2p ?
What is the period?
What type of shift occurs?
Describe the shift.
34.
y = 5sin.25(x)- 7
What is the min and max point?
What is the amplitude?
How many cycles occur from 0- 2p ?
What is the period?
What type of shift occurs?
Describe the shift.
Write the equation for the function based on the descriptions provided
35.
This sine function’s amplitude is 5. It contains 3 cycles and has been shifted 4 units right.
36.
The cosine function’s maximum point is 9 and minimum point is -3. 1 cycle occurs and
there was no horizontal shift.
37.
The amplitude of this sine function is 8. There are no shifts and the period is 5p .
Answer each question about y = sinq or y = cosq
38. In y = sinq , find y if q = 60
39. In y = sinq , find q if y = .707
40. In y = sinq , find three angles in which y = .866
41. In y = cosq , find y if q = 30
42. In y = cosq , if y = .5, find q
43. In y = cosq , find two angles from 0 to 360 in which y = .707