Double Angle Identities Worksheet
Practice problems for understanding and applying double angle identities in trigonometry for Grade 9 students.
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Double Angle Identities Practice
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Read each question carefully and answer to the best of your ability. Show all your work for full credit.
1. The double angle identity for sine is sin(2θ) = .
2. One form of the double angle identity for cosine is cos(2θ) = .
3. The double angle identity for tangent is tan(2θ) = .
4. Which of the following is NOT a form of the double angle identity for cos(2θ)?
cos²θ - sin²θ
2cos²θ - 1
1 - 2sin²θ
2sinθcosθ
5. If sin(θ) = 3/5 and θ is in the first quadrant, find the exact value of sin(2θ).
6. If cos(θ) = -12/13 and θ is in the second quadrant, find the exact value of cos(2θ).
7. The identity tan(2θ) = (2tanθ) / (1 - tan²θ) is valid for all values of θ.
True
False
8. The expression 2sin(15°)cos(15°) is equal to sin(30°).
True
False
Match the trigonometric expression with its equivalent double angle identity.
9. 2sin(x)cos(x)
a. cos(2x)
10. cos²(x) - sin²(x)
b. sin(2x)
11. (2tan(x)) / (1 - tan²(x))
c. tan(2x)
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