Download Practice - SD308.org

NAME
DATE
12-3
PERIOD
Practice
Trigonometric Functions of General Angles
The terminal side of θ in standard position contains each point. Find the exact
values of the six trigonometric functions of θ.
1. (6, 8)
3
4
sin θ = −
, cos θ = −
,
2 √
29
29
20
21
sin θ = −
, cos θ = - −
,
5
5
5
4
tan θ = − , csc θ = −
,
3
4
5
3
sec θ = −
, cot θ = −
3
4
5 √
29
29
3. (-2, -5) sin θ = - − ,
2. (-20, 21)
29
21
tan θ = - −
, csc θ =
20
29
sec θ = - −
, cot θ =
20
cos θ = - − ,
29
29
,
−
21
20
-−
21
√
29
5
tan θ = −
, csc θ = - − ,
5
√
29
2
sec θ = - − , cot θ = −
5
2
2
Sketch each angle. Then find its reference angle.
3π
−
13π
4. −
8
5. -210°
8
7π
6. - −
30°
4
π
−
4
y
y
y
13π
8
θ°
θ°
O
x
O
O
x
θ°
x
- 7π
4
-210°
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Find the exact value of each trigonometric function.
7. tan 135° -1
8. cot 210°
5π
3
- √
11. tan −
3π
12. csc - −
3
(
4
√
3
)
9. cot (-90°)
0
√2
2
√3
−
3
10. cos 405°
−
13π
2 13. cot 2π undefined 14. tan −
- √
6
15. LIGHT Light rays that “bounce off ” a surface are reflected
by the surface. If the surface is partially transparent, some
of the light rays are bent or refracted as they pass from the
air through the material. The angles of reflection θ1 and of
refraction θ2 in the diagram at the right are related by the
, find the
equation sin θ1 = n sin θ2. If θ1 = 60° and n = √3
measure of θ2. 30°
air
θ1
θ1
surface
θ2
800 N
16. FORCE A cable running from the top of a utility pole to the
ground exerts a horizontal pull of 800 Newtons and a vertical
3 Newtons. What is the sine of the angle θ between the
pull of 800 √
cable and the ground? What is the measure of this angle?
800
3N
√3
2
−; 60°
Chapter 12
20
Glencoe Algebra 2