Algebra 2
Chapter 13
Test Review
Name
Period
Date
1. Find the six trigonometric functions of A in the following triangle. Give exact
answers and round to the nearest thousandth.
sin A
A
csc A
25
cos A
sec A
tan A
cot A
B
7
C
2. Solve each triangle. Give angle measures to the nearest degree and side lengths to the
N
nearest tenth. Circle your answers.
E
3
a.
b.
M
F
mE
_____
mP _____
73
10.2
P
G
5
EF = _____
mN _____
GF = _____
PN = _____
3. For each angle, find all coterminal angles such that -360 <  < 360.
a. 77
b. -120
c. 845
4. For each angle, find the reference angle. (Hint: draw a picture.)
a. -120
b. 612
c. -295
5. Find the exact value of the six trigonometric functions of  given each point on the
terminal side of  in standard position.
a. (3, -4)
b. (-2, -6)
sin  =
sin  =
cos  =
cos  =
tan  =
tan  =
csc  =
csc  =
sec  =
sec  =
tan  =
tan  =
6. Given the quadrant of  in standard position and a trigonometric function value of ,
find the exact values for the indicated function.
4
2
a. II, sin  = ; cos 
b. III, tan  = ; csc 
7
5
8. Find the exact values of sine, cosine, and tangent of each angle (without using your
calculator.)
a. -315
b. 225
c. 390
sin  =
sin  =
sin  =
cos  =
cos  =
cos  =
tan  =
tan  =
tan  =
10. Evaluate each inverse trig function. Give your answer in both radians and degrees.

3
Sin-1  

 2 
 1
Cos-1   
 2
 3
Tan-1 

 3 
Sin-1 (1)
________
________
________
________ ________ ________
11.
Solve each equation to the nearest tenth.
a.)
sin  = -0.204 for 90o    270o
b.)
Cos-1 (0)
Tan-1
 3
cos  = 0.778 for 180o    360o
Review #2:
Use the unit circles to give the exact answer for the following:
1. cos -150 = _______
7
= ________
6
2. sin 330 = _______
3. cos 
5. cos -135 = _______
6. sin 225 = ________
7. tan 32 = _______
8. sec  =
9. csc -315 = _______
10. csc -45 = _______
11. cot 23 = _______
13. tan 300 = _______
14. csc
16. tan 60 = _______
17. cot 5 = _______
4. sin
 2 = _______
_______
3
= _______
4
12. sec
 6 = ________
15. cot 240 = ________
18. sec
5
= ________
6
In problems 22-24, select the best answer. (Hint: look at a coordinate plane.)
22. If sin  = cos , in which quadrant(s) may angle  lie?
A. I only
B. II only
C. I or III
23. If cos  > 0, then which of the following must be true?
A. sin  > 0
B. tan  > 0
C. sec  > 0
D. II or IV
D. csc  > 0
24. If sin  tan  > 0 and tan  > 0, which of the following must be true?
A. cos  > 0
B. cos  < 0
C. sec  < 0
D. cot  < 0
22.
23.
24.
25. A car is traveling at the rate of 60 miles per hour (88 feet per second). The radius of its
tires is 15 inches. Determine the measure of the angle through which the wheel turns in 3
seconds.
25.
26. The measure of the angle of elevation to the top of a monument, taken at a point 325 feet
from the foot of the monument is 27. Find the height of the monument.
27. Two buildings of unequal height are on opposite sides of a highway that is 110 feet wide.
From the top of the shorter building, the angle of elevation to the top of the taller building
measures 27 and the angle of depression to the bottom of the tall building measures 22. Find
the height of both buildings.
Review #3:
1.) John is adding a curved edge to the landscaping in front of the high school. The curve is
an arc of a circle with a radius of 1600 feet. The central angle that intercepts the curve

measures radians. Find the length of the curve to the nearest foot.
8
2.) San Antonio, Texas is located about 30o north of the equator. If Earth’s radius is about
3959 miles, approximately how many miles is San Antonio from the equator?
3.) Find the area of the triangle. Round to the nearest tenth.
4.) Solve the triangle. Round to the nearest tenth.
r
Q
5.)
Use the given measurements to solve ∆ABC. Round to the nearest tenth.
a = 8, b = 9, c = 7
6.)
Determine the number of triangular quilt pieces that can be formed by using the
measurements a = 14 cm, b = 20 cm, and mA = 39°. Solve each triangle. Round to the
nearest tenth.
7.)
Use the given measurements to solve ∆ABC. Round to the nearest tenth.
b = 23, c = 18, m  A = 173°
8.)
The surface of a hotel swimming pool is shaped like a triangle with sides measuring 50 m,
28 m, and 30 m. What is the area of the pool’s surface to the nearest square meter?