13-1 Practice

NAME
DATE
13-1
PERIOD
Practice
Trigonometric Identities
Find the exact value of each expression if 0° < θ < 90°.
5
1. If cos θ = −
, find sin θ.
12
−
13
1
2. If cot θ = −
, find sin θ.
13
2 √5
−
5
2
2
, find cot θ.
4. If tan θ = −
3. If tan θ = 4, find sec θ.
5
−
√
17
5
2
Find the exact value of each expression if 180° < θ < 270°.
15
5. If sin θ = - −
, find sec θ.
3
6. If csc θ = - −
, find cot θ.
17
17
-−
8
2
√5
−
2
Find the exact value of each expression if 270° < θ < 360°.
3
7. If cos θ = −
, find cot θ.
8. If csc θ = -8, find sec θ.
10
8 √7
21
3 √
91
91
−
-−
1
10. If cos θ = −
, find cot θ.
1
, find sin θ.
9. If tan θ = - −
3
2
√2
-−
4
√
5
-−
5
Simplify each expression.
14. cot2 θ + 1
sec θ
csc2 θ
17. sin θ + cos θ cot θ
csc θ
sin2 θ
12. −
2
tan θ
cos2 θ
2
θ - cot2 θ
−
15. csc
2
1 - cos θ
csc2 θ
cos θ
cos θ
- −
18. −
1 - sin θ
1 + sin θ
13. sin2 θ cot2 θ
cos2 θ
θ - sin θ
−
16. csc
cot θ
cos θ
19. sec2 θ cos2 θ + tan2 θ
sec2 θ
2 tan θ
20. AERIAL PHOTOGRAPHY The illustration shows a plane taking
an aerial photograph of point A. Because the point is directly below
the plane, there is no distortion in the image. For any point B not
directly below the plane, however, the increase in distance creates
distortion in the photograph. This is because as the distance from
the camera to the point being photographed increases, the
exposure of the film reduces by (sin θ)(csc θ - sin θ). Express
(sin θ)(csc θ - sin θ) in terms of cos θ only. cos2 θ
θ
A
B
21. WAVES The equation y = a sin θt represents the height of the waves passing a buoy at
a time t in seconds. Express a in terms of csc θt. a = y csc θt
Chapter 13
8
Glencoe Algebra 2
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
11. csc θ tan θ

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