WORKSHEET – SIN 2A and COS 2A - Humble … 3-5 Name_____ Date_____ Period____ WORKSHEET – SIN 2A...

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A 3-5 Name__________________________________Date______________Period____ WORKSHEET – SIN 2A and COS 2A Simplify the given expressions. 1. 2 sin 10º cos 10º 2. cos 2 15º - sin 2 15º 3. sin 40º cos 40º 4. cos 2 x - 1 5. 5 – 10 cos 2 θ 6. cos 55º cos 35º - sin 55º sin 35º 7. 1 – sin 2 x 8. 1 – 2 sin 2 x 9. 2 sin 3α cos 3α 10. 2 cos 2 θ - 2 sin 2 θ 11. sin 20º cos 15º - cos 20º sin 15º 12. sin140° cos40°+cos140° sin 40° 13. 2 cos 2 25º - 1 14. 10 sin x cos x 15. sin 2x cos 2x 16. 4 - 8 sin 2 x 17. cos 2 5θ - sin 2 5θ 18. 1 – 2 sin 2 45º 19. cos 25°cos 15° - sin 25° sin 15° 20. x sin 2 x 2 sin

Transcript of WORKSHEET – SIN 2A and COS 2A - Humble … 3-5 Name_____ Date_____ Period____ WORKSHEET – SIN 2A...

Page 1: WORKSHEET – SIN 2A and COS 2A - Humble … 3-5 Name_____ Date_____ Period____ WORKSHEET – SIN 2A and COS 2A Simplify the given expressions. 1. 2 sin 10º cos 10º 2. cos 2 15º

A 3-5

Name__________________________________Date______________Period____

WORKSHEET – SIN 2A and COS 2A

Simplify the given expressions.

1. 2 sin 10º cos 10º 2. cos2 15º - sin2 15º

3. sin 40º cos 40º 4. cos2 x - 1

5. 5 – 10 cos2

θ 6. cos 55º cos 35º - sin 55º sin 35º

7. 1 – sin2 x 8. 1 – 2 sin2 x

9. 2 sin 3α cos 3α 10. 2 cos2 θ - 2 sin2 θ

11. sin 20º cos 15º - cos 20º sin 15º 12. sin140° cos40°+cos140° sin 40°

13. 2 cos2 25º - 1 14. 10 sin x cos x

15. sin 2x cos 2x 16. 4 - 8 sin2 x

17. cos2 5θ - sin2 5θ 18. 1 – 2 sin2 45º

19. cos 25°cos 15° - sin 25° sin 15° 20. xsin2

x2sin

Page 2: WORKSHEET – SIN 2A and COS 2A - Humble … 3-5 Name_____ Date_____ Period____ WORKSHEET – SIN 2A and COS 2A Simplify the given expressions. 1. 2 sin 10º cos 10º 2. cos 2 15º

A 3-5

Verify the following identities.

21. 0sin)-cos( =

++ θ

πθπ

2 22.

θ

θ

θ

θ

cos

sin1

sin1

cos −=

+

23. cos4

θ – sin4θ = cos 2θ 24. (sinx + cosx)2 – 1 = sin2x

Use the information given about the angle to find the exact value of a) sin 2θ, and b) cos 2θ.

25. tan θ = 2

1, π<θ<π 2 26. cos θ =

3

6− , 0 < θ < π

ANSWERS: 1. sin20º 2. 2

3 3. °80sin

2

1 4. –sin

2x 5. -5cos2x 6. 0 7. cos

2x 8. cos2x 9. sin6α 10. 2cos2 θ

11. sin5º 12. 0 13. cos50º 14. 5sin2x 15. x4sin2

1 16. 4cos2x 17. cos10 θ 18. 0 19. cos40º 20. cosx

21 – 24. Proofs 25. a) 5

4 b)

5

3 26. a)

3

22− b)

3

1


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