Double and Half Angle Identities Worksheet
Explore and apply double and half angle identities to simplify trigonometric expressions and solve equations.
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Double and Half Angle Identities
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Date:
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Read each question carefully and answer to the best of your ability. Show all your work for full credit.
1. Which of the following is equivalent to sin(2x)?
2sin(x)cos(x)
sin(x) + cos(x)
2sin(x)
cos(2x)
2. If cos(θ) = 3/5 and θ is in Quadrant I, what is sin(2θ)?
24/25
7/25
12/25
6/5
3. The identity for cos(2x) can be expressed as cos²(x) - sin²(x), or , or .
4. The half-angle identity for sin(x/2) is ±√((1 - cos(x)) / ).
5. Given tan(θ) = -4/3 and θ is in Quadrant II, find the exact value of sin(θ/2).
6. The identity tan(2x) = (2tan(x))/(1 - tan²(x)) is always true for all values of x.
True
False
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