Chapter 5 & 6 Practice Problems
Directions:
Make sure you follow the instructions pertaining to using a calculator or not
1. Name the reference angle: 135°
2. Name the reference angle: 280° 40′
Use a calculator to find each of the following:
3. csc 345° 20′
4. sec 56.3°
5. cot (-315.5°)
Use a calculator to find θ to the nearest tenth of a degree if is θ is between 0° and 360° and:
6. sin θ = -0.3456 with θ in QIII.
7. sec θ = 3.2442 with θ in QIV.
Give the exact value of each of the following:
8. tan 135°
9. cos 210°
12. Convert 105° to radian measure.
13. Convert

14. sin (- )
16. cos (-
6
15. sin
10. csc 315°
11. sec 300°
2
17. cot
3
18. Find the length of the arc S cut off by a central angle of
8cm.
3
4
11
12
to degree measure.
)

3

6
radians in a circle where r =
19. Find the area of the sector of a circle formed by a central angle of 120° in a circle of
radius 9 inches.
Solution for Chapter 3
1.
2.
3.
4.
5.
6.
7.
45°
79°20
-3.9495
1.802
1.018
200.2°
288.0°
8.
-1
14. -1/2
9.
-
15.
10.
11.
12.
13.
2
7/12
165°
16. 17.
18.
19.
Chapter 5 Practice Problems
Directions: Make sure you follow the directions for graphing and label each intercept and
change of direction.
Graph each function on the given interval.
1. y = sec x, between x =

2
3
and
2
.
2. y = cot x, between x = 0 and 2.
Sketch one complete cycle of each graph. Show your work for finding amp, period, phase and
vertical shift. Label the axes so that the amp, period, phase and tick marks can be easily read.
6. y = 2 sin 2
1
3. y = cos x
2

7. y = 4 cos (   )
2
4. y = - sin 2 

1
3
8. y = 4 sin ( 2   )
5. y = 3 cos 
4
9. Sketch the graph of y = 2 + sin x, for x between 0 and 2
10. Sketch the graph of y = 2x + 2sin x, for x between 0 and 4
11. Write a description explaining how to graph y  2sin 2  x . Write as if you were explaining to
another student who does not know about graphing. Use complete sentences and be as neat
as possible.
Solutions for Chapter 5
1.
2.
3.
4.
5.
6.
7.
graph
graph
graph
graph
graph
graph
graph
8. graph
9. graph
10. graph
.
Chapter 6 Practice Problems
Directions: Make sure you pay attention to whether you are working with a right triangle or not.
Also, be aware of which part of the triangle you are being asked to find.
1.
Find the stated piece of each triangle given the following information
a. Given a triangle with A  102, B  23, and
b. Given a triangle with B  56, a  98, and
c  576.1,
find
a.
b  85 , find the two possible values of C
.
c. Given a triangle with a  135, b  71.6, and
c  69,
find
B.
2. A boat leaves a port and sails 16 miles at a bearing of S 20 E . Another boat leaves the same
port and sails 12 miles at a bearing of S 60 W . How far apart are the two boats at this point?
Solutions for Chapter 6
1a. a = 687.9
1b. C1 = 51o ,C2 = 17o
1c. B = 16.5o
2. 18.3miles
.