Download Chapter 5 – More Practice

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Chapter 5 Review
1. Give the angle measure represented by:
a. 2.7 rotations counterclockwise
b) 16.3 rotations clockwise
2. What is the difference between a coterminal angle and a reference angle?
3. Identify all angles that are coterminal with each angle below. Then find one
positive angle and one negative angle that are coterminal with this angle.
a) 765
b) –240
c) 217°
4. Find the angle measure of the reference angles for the following angles:
a) 316°
b) -775°
c) 230
d) - 128
e) -77
f) 320
g) -225
h) -330
5. Find 6 trig ratios for <F. Leave your answers in simplest radical form.
For problem 6-7, refer to the figure below. Find each value to the nearest tenth.
A
6. Find a
c = 7.3
b
7. Find b
60
C
B
8. Find the values of the 6 trig. functions for angle  in standard position if the
point (-6, 7) lies on its terminal side. Leave your answers in simplest radical
form.
9. Find the value of csc in standard position whose terminal side is the point:
a) (-6, 2)
b) (3, -6)
10. If tan 
 0.375 , find cot  .
11. A person in a hot-air balloon observes that the angle of depression to a building
on the ground is 65.8°. After ascending vertically 500 feet, the person now
observes that the angle of depression is 70.2°. How far is the balloonist now from
the building?
12. The San Jacinto Column in Texas is 570 feet tall and, at a particular time, casts a
shadow 700 feet long. Find the angle of elevation to the sun at that time.
No Calculator
13. Evaluate. Give the exact answer.
a) cos(-180)
b) sec (270)
c) csc (-90°)
d) cot (180)
e) tan 315
f) sin 240
g) cot (-225°)
h) csc -210°
i) sec -330°
14. Suppose an angle  is in standard position with the terminal side lying in
Quadrant IV. If sin 

 2
, determine the value of cos 
2
15. Solve each equation if 0° 
x  360°
1
2
a) tan x =  3
3
b) sin x =
d) csc x  1
e) csc x   2
c) sec x 
2 3
3
f) sec x  2
16. Find the following:
8
a) If sec  
, find cos . (for 0< < 360)
7
b) If tan  
17. a) If sin  
2
, find sin 
3
3
, find csc 
2
(for 0< < 360)
b) If cos 
 2
, find sec 
2
18. Suppose  is an angle in standard position whose terminal side lies in quadrant II.
If sin  = 4/7, find
a. The value of cos 
b. The value of tan .
19. Assuming an angle is in Quadrant III , evaluate:
12 

sin  sec 1  
7

3

20. Assuming an angle is in Quadrant IV, evaluate: csc tan 1  
5

4

21. Assuming an angle in Quadrant I, evaluate tan  arccos  .
5

9

22. Assuming an angle in Quadrant II, evaluate sec  arc csc  .
7

Don’t forget to review and know your Unit Circle well! Forward and Backward…. 