Double Angle Identities

Front

What is the double angle identity for sine?

Back

sin(2θ) = 2sin(θ)cos(θ)

Front

What is the double angle identity for cosine?

Back

cos(2θ) = cos²(θ) - sin²(θ) or cos(2θ) = 2cos²(θ) - 1 or cos(2θ) = 1 - 2sin²(θ)

Front

If sin(θ) = 3/5, what is cos(θ) in the first quadrant?

Back

cos(θ) = 4/5 (using the Pythagorean identity: sin²(θ) + cos²(θ) = 1)

Front

Calculate sin(2θ) if sin(θ) = 3/5 and θ is in the first quadrant.

Back

sin(2θ) = 2sin(θ)cos(θ) = 2 * (3/5) * (4/5) = 24/25

Front

If sin(x) = 12/13, what is cos(x) in the first quadrant?

Back

cos(x) = 5/13 (using the Pythagorean identity: sin²(x) + cos²(x) = 1)

Front

Calculate sin(2x) if sin(x) = 12/13 and x is in the first quadrant.

Back

sin(2x) = 2sin(x)cos(x) = 2 * (12/13) * (5/13) = 120/169

Front

What is the range of θ for the double angle identities?

Back

0 ≤ θ < 2π

Front

If cos(θ) = 4/5 and θ is in the fourth quadrant, what is sin(θ)?

Back

sin(θ) = -3/5 (since sin is negative in the fourth quadrant)