Download Trigonometry

Trigonometry Review
 Solve all problems.
 Check your answers with the key provided after the questions.
 If you need help reviewing some topics, enroll in a section of TU 301
designated for use of the Math Center and get help at the Center.
1.
Convert 21 4216 to decimal in degrees.
2.
Convert 210  to radians.
3.
Convert
4.
If   60  is a central angle in a circle of radius 8 ft, find the length of the arc cut by 
and the area of the sector determined by the angle.
5.
If (12, -5) is a point on the terminal side of an angle  in standard position, find the exact
values of the six trigonometric functions of  .
6.
Find the exact value of
7.
Graph y  3 sin(2 x   ) for one period. Label the axes appropriately.
8.
Find the exact value of each expression. Do not use a calculator.
1
a. sin 1   
2
7
to degrees.
4
 1
b. cos 1    
 2
c. tan1 ( 3 ) 

 1 
d. sin  cos 1     
 3 

sin(20  )
 tan 200  .
cos(380  )
9.
Use a calculator to find the value of each expression. Work in radians and round your
answers to four decimal places.
a. cos 1 ( 0.8) 
b. tan 1 (0.2) 
c. csc 1 (3) 
d. sin 1 (0.35) 
e. cot 1 (4) 
10.
11.
 7 
Find the exact value of cos
.
 12 
3
3
 
If sin    ,    
, find the exact value of sin   .
5
2
2
12.
Establish the identity sin(   )  sin(   )  2 sin  cos  .
13.
Solve the equation cos(2 ) 
13.
Solve the triangle having a  3, c  2,   110 .
14.
Solve the triangle having a  2, b  3,   60 .
15.
A ship, offshore from a vertical cliff known to be 100 feet in height, takes a sighting of the
top of the cliff. If the angle of elevation is found to be 25  , how far offshore is the ship?
16.
Find polar coordinates for the point with rectangular coordinates ( 3, 3 ) .
1
, 0    2 .
2
19.
 2 
Find the rectangular coordinates for the point with polar coordinates  5,

 3 
 2 
Plot the point given in polar coordinates.  3,

 3 
Plot the point given in polar coordinates. (2, 135 )
20.
Identify and graph the polar equation r = 3.
17.
18.
Trigonometry Review
KEY
1.
2.
3.
4.
5.
6.
7.
21.704 o
7
6
315o
8
32 2
s
ft, A 
ft
3
3
5
12
5
12
13
13
sin  
, cos   , tan    , cot    , sec   , csc   
13
13
12
5
12
5
0
2 2

2

(b)
(c)
(d)
3
3
6
3
9. (a) 2.4981 (b) 0.1974 (c) 0.3398 (d) 0.3576 (e) 0.2450
 6 2
10.
4
3
3 10
or
11.
10
10
12. sin(   )  sin(   )  sin  cos   cos  sin   sin  cos   cos  sin   2 sin  cos 
13. a  3,   42.972o , b  4.135,   110o , c  2,   27.028o
14. No such triangle
15. 214.451 ft
8. (a)
3
7

 

16.  6 ,
 2k  or  - 6 ,
 2k 
4
4

 

 5 5 3

17.   ,

2
2


18.
19.
20. Circle, center at (0, 0) and radius 3.