PCH-2.6 Double Angle Formulas

Front

What is the double angle formula for sine?

Back

sin(2θ) = 2sin(θ)cos(θ)

Front

What is the double angle formula for cosine?

Back

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

Front

What is the double angle formula for tangent?

Back

tan(2θ) = 2tan(θ) / (1 - tan²(θ))

Front

Simplify sin(2θ) using the double angle formula.

Back

sin(2θ) = 2sin(θ)cos(θ)

Front

Simplify cos(2θ) using the double angle formula (first version).

Back

cos(2θ) = cos²(θ) - sin²(θ)

Front

Simplify cos(2θ) using the double angle formula (second version).

Back

cos(2θ) = 2cos²(θ) - 1

Front

Simplify cos(2θ) using the double angle formula (third version).

Back

cos(2θ) = 1 - 2sin²(θ)

Front

If sin(θ) = 1/2, what is sin(2θ)?

Back

sin(2θ) = 2(1/2)(√3/2) = √3/2

Front

If cos(θ) = √3/2, what is cos(2θ)?

Back

cos(2θ) = 2(√3/2)² - 1 = 1/2

Front

If tan(θ) = 1, what is tan(2θ)?

Back

tan(2θ) = 2(1)/(1 - 1²) = undefined (as it approaches infinity)