Download Problem Set 17

Pre-calculus: Problem Set 17
Trigonometry
4
3
Convert from radian measure to degree measure.
1.
Convert from degree measure to radian measure.
3. 210
2.
7
4
4. 135
Evaluate the following using exact values. (Do not use a calculator.)

5.
sin
8.
sec
11.
tan1  3
14.
 2 
arcsin  sin 
3 

6
5
3



 2 
17. cos 2 sin 1   
 3 

20. cos 75
6.
csc 270
9.
tan
5
4
7.
cos135
10.
cot 180
12.

3

arcsin  

2


5 

13. cos 1  cos 
4

15.

 2 
tan cos 1   
 5 


3

16. sin  cos 1

2


18.

 1 
sin 2 cos 1   
 3 

19. sin15
Find the values of the remaining 5 trigonometric functions of angle θ given
4
5
21. cos   
and cot   0
22. tan   and sin   0
3
3
Simplify.
23. cosx  
24. sin90  x 
Write each trigonometric expression as an algebraic expression.
1

25. sec tan1 x
26. sin arctan 
x



3
1
Given sin x   , x is a Quadrant IV angle, and y  cos 1   , find
5
 3
27. cos x
28.
29.
cosx  y 
sin y
Solve.
30. sec    2
32.
3 tan x  1  0
0    360
31. sin   
0 x
33. sin 2 x 
3
2
0    2
1
sin 2 x 0  x  2
2
Give the domain and range for each of the following and sketch a graph.
34. f ( x)  sin x


36. y  4 sin 3x  
2

35. g ( x)  tan x


37. For y  4 sin 3x   , find the amplitude, period and horizontal displacement(phase
2

shift).
Solutions to Odd Problems:
4 180 

 240 
3

2
7. cos 135  
2
13.
1.
5 

cos 1  cos

4 


2

cos 1  

2


3
4
3. 210  
9. tan

180

7
6
5. sin

6


5
1
4
1
2

11. tan 1  3  
15.

3
17.

 2 
tan cos 1   
 5 

2
Let cos 1  
5
adjacent side  2

 2 
cos 2 sin 1   
 3 

2
2
Let sin 1     , sin  
3
3
hypotenuse  5
2
cos 2  1  2 
3
1
cos 2 
9
cos 2  1  2 sin 2 
opposite side  21
tan  
19.

21
2
2
21.
sin 15
One possible way :
sin 15   sin(45  30) 
 sin 45  cos 30   cos 45  sin 30 
2 3
2 1



2 2
2 2
6 2

4

5
and cot   0
3
 is in Quadrant III
cos   
sin 2   1  cos 2   1 
5 4

9 9
2
5
2 5
sin    , cot  
, tan  
3
2
5
3 5
3
sec  
, csc  
5
2
23.  cos x
25.
27.

sec tan 1 x
sin 2 x  cos 2 x  1

9
 cos 2 x  1
25
16
cos 2 x 
25
4
cos x 
5
tan 1 x  
Let
sec 2   1  tan 2 
sec   1  x 2


or sec tan 1 x  1  x 2
31. θ = 4π/3, 5π/3
29.
33.
1
sin 2 x
2
sin 2 x  12 (2 sin x cos x)
sin 2 x 
cos( x  y )  cos x cos y  sin x sin y
sin 2 x  sin x cos x  0
 4  1    3  2 2 
     

 5  3   5  3 
sin x(sin x  cos x)  0
sin x  0 or sin x  cos x
46 2

15
x  0, 
or
x
 5
4
,
4
5 
 
0, ,  , 
4
 4



35. D:  x x   k , k is an integer 
2


R:  , 
y
37. Amplitude = 4
Period = 2π/3
Phase Shift = π/6 units to the left
Answers to Even Problems:
2. 315o
4. 3π/4
8. 2
10. undefined
14. π/3
20.
6 2
4
24. cos x
x
6. -1
12. –π/3
4 2
18.
9
16. ½
(Each block is 1 unit.)
22. cot θ = ¾, sin θ = -4/5, cos θ = -3/5, csc θ = -5/4, sec θ = -5/3
26.
1
28.
2 2
3
x 1
32. x = 5π/6
34. D:  ,  R: [-1, 1]
See next page for graphs.
2
30. θ = 135o, 225o
36. D:  ,  R: [-4, 4]
34.
36.
y
y
3
1
π
x
x
π