Download Name

Name:
Date:
Advanced Math
Trigonometric Functions – Review
I. Find sin t, cos t, and the tan t when the terminal side of an angle of t radians passes
through the given point.
1.
(-3, 2)
2.
(4, -3)
II. Find sin t, cos t, and the tan t when the terminal side of an angle of t radians passes
through the given point on the unit circle.
 1
3 

,

10 
 10
3.
 3 4
  , 
 5 5
4.
III. Identify an angle 0  t   that is coterminal with the given angle, and find the sine
and cosine of the given angle.
9
2
5.

6.
7
4
IV. Identify the quadrant of the terminal side of the angle of t radians. Then determine
the sign of sin t, cos t, tan t.
7. 11
8. -23 
9. 6.4
10.

17
V. Sketch each angle whose radian measure is given and find its reference angle.
11.
7
3
12.
6
5
13. 
3
4
VI. Find the exact value of the sine, cosine, and tangent of each radian value.
14.
7
6
15.
18.
11
6
19. 
17
3
10
3
16.
5
4
20. 
25
4
17. 3
21.  
Name:
Date:
Advanced Math
VII. Write each expression as a single real number.





2
22. sin ( ) cos ( ) - cos ( ) sin ( )
23. cos ( ) cos ( ) + sin ( ) sin ( )
6
2
6
2
2
3
24. sin (
3
5
3
5
) cos ( ) - cos ( ) sin ( )
4
6
4
6
25. sin (
7
5
7
5
) cos ( ) + cos (  ) sin ( )
3
4
3
4
Answers:
2
1. r  13 sin t 
13
cos t  
3
13
tan t  
2
3
3
4
3
cos t 
tan t  
5
5
4
4
3
4
3
1
cos t  
tan t 
4. sin t  
sin t  
cos t 
tan t  3
5
5
3
10
10

9
9

7
1
7
1
; cos
 0 sin
1
; cos(  ) 
6.
sin(  ) 
2
2
2
4
4
4
2
2
QIV : sin t is -, cos t is +, tan t is –
Negative x-axis: sin t is 0, cos t is -, tan t is 0
9. QI: all positive
2. r  5 sin t  
3.
5.
7.
8.


12. ref. angle =
3
5

7
1
7
3
7
1
ref. angle =
14. sin
  ; cos

; tan

4
6
2
6
2
6
3
17
3
17 1
17
sin

; cos
 ; tan
 3
3
2
3
2
3
5
1
5
1
5
sin

; cos

; tan
1
4
4
4
2
2
sin 3  0; cos 3  1; tan 3  0
10. QI: all positive
13.
15.
16.
17.
11. ref. angle =
11
1
11
3
11
1
  ; cos

; tan

6
2
6
2
6
3
10
3
10
1
10
)
; cos( 
)   ; tan( 
) 3
19. sin( 
3
2
3
2
3
25
1
25
1
25
20. sin( 
)
; cos( 
)
; tan(
)  1
4
4
4
2
2
18. sin
21. sin(  )  0; cos(  )  1; tan(  )  0
23.
1
2
24.
1 3
2 2

6
2

4
4
3
2
22. 
25.
1 3
2 2

6
2

4
4