Double and Half Angle Identities Worksheet
Explore and apply double and half angle identities to solve trigonometric problems at a Grade 10 level.
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Double and Half Angle Identities
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Read each question carefully and answer to the best of your ability. Show all your work for full credit.
1. If sin θ = 3/5 and θ is in the first quadrant, find the exact value of sin(2θ).
2. Given cos θ = -5/13 and θ is in the second quadrant, find the exact value of cos(2θ).
3. The double angle identity for tan(2θ) is tan(2θ) = .
4. If cos(2θ) = 1 - 2sin²θ, then sin²θ = .
5. If cos θ = 1/2 and θ is in the first quadrant, find the exact value of cos(θ/2).
6. Given sin θ = -√3/2 and θ is in the third quadrant, find the exact value of sin(θ/2).
7. The identity sin(2θ) = 2sinθcosθ is always true for all values of θ.
True
False
8. The half-angle formula for tan(θ/2) always results in a positive value.
True
False
9. Which of the following is an equivalent expression for cos(2θ)?
2sinθcosθ
cos²θ - sin²θ
1 - cos²θ
2cos²θ + 1
10. The sign of √( (1 - cos θ) / 2 ) for sin(θ/2) depends on the quadrant of:
θ
2θ
θ/2
None of the above
11. Prove the identity: (sin 2θ) / (1 + cos 2θ) = tan θ