Worksheet 9
The Unit Circle
Find the point ( x, y ) on the unit circle that corresponds to the real number t.
1. t =
π
4
2. t =
π
3
3. t =
5. t =
2π
3
6. t =
3π
2
7. t = π
7π
6
4. t =
5π
4
8. t = −
4π
3
12. t =
11π
6
Evaluate (if possible) the sine, cosine, and tangent of the real number.
9. t =
π
4
13. t =
3π
4
10. t =
π
3
11. t = −
14. t =
5π
3
15. t =
π
6
π
2
16. t = 2π
Evaluate (if possible) the six trigonometric functions of the real number.
17. t =
π
6
18. t =
7π
4
19. t = −
5π
3
20. t =
3π
2
Answers:
⎛ 2 2⎞
,
⎟
⎝ 2 2 ⎠
⎛1
3⎞
⎟
⎝2 2 ⎠
1) ⎜
2) ⎜ ,
6) ( 0, −1)
7) ( −1, 0 )
π
2
=
4
2
π
2
cos =
4
2
π
tan = 1
4
5π
3
14) sin
=−
3
2
5π 1
cos
=
3 2
5π
tan
=− 3
3
π 1
17) sin =
6 2
π
3
cos =
6
2
π
3
tan =
6
3
π
csc = 2
6
π 2 3
sec =
6
3
π
cot = 3
6
9) sin
π
3
=
3
2
π 1
cos =
3 2
π
tan = 3
3
π
15) sin = 1
2
π
cos = 0
2
π
tan undefined
2
10) sin
7π
2
=−
4
2
7π
2
cos
=
4
2
7π
tan
= −1
4
7π
csc
=− 2
4
7π
sec
= 2
4
7π
cot
= −1
4
18) sin
⎛
3) ⎜ −
⎝
3 1⎞
,− ⎟
2
2⎠
⎛
4) ⎜ −
⎝
2
2⎞
,−
2
2 ⎟⎠
⎛ 1 3⎞
⎟
⎝ 2 2 ⎠
5) ⎜ − ,
⎛ 1 3⎞
⎟
⎝ 2 2 ⎠
8) ⎜ − ,
7π
1
=−
6
2
7π
3
cos
=−
6
2
7π
3
tan
=
6
3
16) sin 2π = 0
cos 2π = 1
tan 2π = 0
11) sin
3
⎛ 5π ⎞
=
⎝ 3 ⎟⎠
2
⎛ 5π ⎞ 1
cos ⎜ − ⎟ =
⎝ 3⎠ 2
⎛ 5π ⎞
tan ⎜ − ⎟ = 3
⎝ 3⎠
19) sin ⎜ −
⎛ 5π ⎞ 2 3
csc ⎜ − ⎟ =
⎝ 3⎠
3
⎛ 5π ⎞
sec ⎜ − ⎟ = 2
⎝ 3⎠
3
⎛ 5π ⎞
cot ⎜ − ⎟ =
⎝ 3⎠
3
11π
1
=−
6
2
11π
3
cos
=
6
2
11π
3
tan
=−
6
3
12) sin
3π
= −1
2
3π
cos
=0
2
3π
tan
undefined
2
3π
csc
= −1
2
3π
sec
undefined
2
3π
cot
=0
2
20) sin
3π
2
=
4
2
3π
2
cos
=−
4
2
3π
tan
= −1
4
13) sin