Double and Half Angle Identities Worksheet
Grade 12 Math worksheet on double and half angle identities, covering derivation, application, and problem-solving.
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Topics
Double and Half Angle Identities
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Read each question carefully and provide your answers using the double and half-angle identities. Show all your work for full credit.
1. The double angle identity for sin(2θ) is .
2. One form of the double angle identity for cos(2θ) is .
3. The half angle identity for tan(θ/2) can be expressed as .
4. If cos(θ) = 3/5 and θ is in Quadrant I, then sin(θ/2) = .
1. Which of the following is equivalent to 2sin(x)cos(x)?
sin(2x)
cos(2x)
tan(2x)
sin(x/2)
2. If tan(θ) = 1/2 and θ is in Quadrant I, what is the value of tan(2θ)?
4/3
-4/3
1/4
-1/4
1. Express sin(θ) in terms of cos(θ/2) using a half-angle identity.
2. Verify the identity: (sin(2x))/(1+cos(2x)) = tan(x).
1. The identity cos(2θ) = 1 - 2sin²(θ) is a double angle identity.
True
False
2. The half-angle identity for cos(θ/2) is always positive.
True
False
1. Given sin(θ) = 4/5 and θ is in Quadrant II, find the exact values of sin(2θ), cos(2θ), and tan(2θ).
2. Use half-angle identities to find the exact value of sin(22.5°).