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3.3 Practice

This document contains practice problems involving trigonometric functions such as sine, cosine, and tangent. There are multiple parts with problems finding function values given angles or coordinates and finding coordinates given function values and angles.

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zyf080424
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84 views5 pages

3.3 Practice

This document contains practice problems involving trigonometric functions such as sine, cosine, and tangent. There are multiple parts with problems finding function values given angles or coordinates and finding coordinates given function values and angles.

Uploaded by

zyf080424
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
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Sine and Cosine

3.3 Function Values


Practice Set 1

Problems 1 − 4, A point on the terminal side of an angle 𝜃𝜃 is given. Find the exact values of the
sine and cosine functions of 𝜃𝜃.

1. (3, −4)

2. (−1, 2)

3. (−1, −1)

4. (5, 12)

Problems 5 −6, Find the values of sin 𝜃𝜃 and cos 𝜃𝜃 of the angle.

5. 6.

6 5
θ θ
8 7

© 2023 Jean Adams Flamingo Math.com


Problems 7 − 12, the measure θ of an angle in standard position is given. Find the exact values of
𝑐𝑐𝑐𝑐𝑐𝑐 𝜃𝜃 and 𝑠𝑠𝑠𝑠𝑠𝑠 𝜃𝜃 for each angle measure.

5𝜋𝜋 3𝜋𝜋
7. 8. 2
3

7𝜋𝜋 2𝜋𝜋
9. 6
10. − 3

5𝜋𝜋 𝜋𝜋
11. 12. − 6
4

Problems 13 -16, Find the exact values of the indicated variables (selected from x, y, and r.)

13. Find x and y 14. Find 𝑥𝑥 and 𝑟𝑟

𝑟𝑟
13 3 5
𝑦𝑦
45°
𝑥𝑥
𝑥𝑥

15. Find 𝑥𝑥 and 𝑦𝑦 16. Find 𝑦𝑦 and 𝑟𝑟

12
𝑦𝑦 𝑟𝑟
𝑦𝑦
30°
60°
𝑥𝑥
8

© 2023 Jean Adams Flamingo Math.com


Sine and Cosine
3.3 Function Values
Practice Set 2

Problems 1− 4, The terminal side of angle 𝜃𝜃 contains the point (𝑥𝑥, 𝑦𝑦). Find exact values of the sine
and cosine functions of 𝜃𝜃. Use radicals, if necessary, but no decimals.

1. (5, 7)

2. (12, −5)

3. (−8, 5)

4. (−15, −8)

© 2023 Jean Adams Flamingo Math.com


Problems 5− 8, Given an angle 𝜃𝜃 in standard position and the radius 𝑟𝑟 centered at the origin, find
the coordinates of point 𝑃𝑃 = (𝑥𝑥, 𝑦𝑦) of the angle where the terminal ray intersects
the circle.
2𝜋𝜋
5. 𝜃𝜃 = 3
, 𝑟𝑟 = 8

−5𝜋𝜋
6. 𝜃𝜃 = 6
, 𝑟𝑟 = 6

3𝜋𝜋
7. 𝜃𝜃 = 4
, 𝑟𝑟 = 4

𝜋𝜋
8. 𝜃𝜃 = − 3 , 𝑟𝑟 = 5

© 2023 Jean Adams Flamingo Math.com


Problems 9− 12, Given key information, find the values of the function specified.

5
9. If 𝜃𝜃 terminates in Quadrant III and tan 𝜃𝜃 = 3
, find sine and cosine of 𝜃𝜃.

3
10. If sin 𝜃𝜃 < 0 and tan 𝜃𝜃 = − 2 , find sine and cosine of 𝜃𝜃 and the coordinates of 𝑃𝑃 = (𝑥𝑥, 𝑦𝑦)

11. Find all values of 0 ≤ 𝜃𝜃 < 2𝜋𝜋 where sin 𝜃𝜃 = 0

12. A 20-foot-long ladder is leaning against a house. The ladder makes a 52° angle with the
ground.

A. How far up the wall does the ladder reach?

B. How far from the wall is the base of the ladder?

© 2023 Jean Adams Flamingo Math.com

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