Download Final Exam Review Questions Trigonometry NOTE: You will be able

Final Exam Review Questions
Trigonometry
NOTE: You will be able to use your calculator for the entire final exam.
Chapter 1:
1) Find sin  , cos , tan  if  is an angle in standard position having the point (–4, 3) on its terminal side.
2) Find tan  and sec  if sin  
12
13
and cos  0 .
3) Use the Pythagorean identities to find sin  , cos , tan  if sec  
5
with  in quadrant IV.
4
4) Convert 70.12 to DMS form.
5) Find the angle of smallest possible positive measure coterminal with 210
Chapter 2:
6) Find the six trigonometric values for the given angle   150
7) Find the six trigonometric values for the given angle   420
8) Evaluate the expression and give the exact value. cos 2 45  2 sin 150
9) Find the decimal approximation of cos 425 32'
10) Find the decimal approximation of sec 95.29
11) A radio technician is at a spot that has an angle of elevation of 18.5 to the top of a 255-foot-tall
transmitting antenna. How far is the radio technician from the base of the transmitting antenna?
12) Find the reference angle for 522.87
13) Use a calculator to find the decimal approximation for csc 132 44'
Chapter 3:
14) Convert 225 to radians.
15) Convert
11
to degrees.
6
16) Give the exact value of tan
9
.
4
17) Give the exact value of cos 135 =
18) Give the exact value of sec
5

3
19) Use a calculator to find cot 5.2398
20) Find the arc length in the figure below.
21) Find the radius of a circle in which the central angle of 2 radians intercepts an arc of length 3 feet.
Chapter 4:
22) What is the period of y  3  2 sin

x?
4
23) Graph one period of each of the following. State the amplitude (A), period (P), vertical shift (V.S.), and
phase shift (P.S.). Show all critical points as well as labeling the axes.
a. y  3  3 cos x

1
b. y  2  3 cos  x  
2
2

3
c. y   sin  x    1
2
2
 
d. y  csc x 
4 
1

e. y  cot  x  
2
2


f. y  4 sec x  
2

Chapter 5:
24) Use the sum and difference identities to find the exact value of :
cos
5
12
   5 
  

 4 6 12 
5
4
with x in quadrant III and sin y   with y in quadrant IV, find:
5
5
a. sin (x – y)
25) Given that cos x  
b. cos (x – y)
26) Verify the following identities
a. 2 cot x sin x cos x  2  2 sin 2 x
b. cos 2 x sec x  2 cos x  sec x
cos x  cos3 x
c.
 sin x cos x
sin x
d. (1  cos 2 x )(1  cos2 x )  2 sin 2 x  sin 4 x
e.
sin x
 cot x  csc x
1  cos x

 1  tan x
f. tan  x  
4
 1  tan x
Chapter 6:
27) Give the exact radian value for each of the following.
 1
a. cos1 
 2 
 
b. sec 1 2
c. tan 1
3
3
 3

d. sin 1

 2 
28) Give the exact degree value for each of the following. Round your answers to 2 decimal places.
a. sec 1 (3)
b. csc 1 (5.5)
c. cot 1 (.78643)
29) Solve each equation for solutions 0, 2  .
a. 2 cos4 x  cos 2 x
b. 41  sin x 1  sin x   3
c. cos 2 x  cos x  0
Chapter 7:
30) Use the law of sines and/or law of cosines to solve the following triangles:
a. A  37
B  48 c  18
b. C  28.3
a  5.71 b  4.21
c. a = 16
b = 17
c = 19
31) Two lighthouses are located on a north-south line. From lighthouse A, the bearing of a ship 2742 meters
away is 11141 . From lighthouse B, the bearing of the ship is 3251 . Find the distance between the
lighthouses.