Double Angle Identities

Front

What is the Double Angle Identity for sine?

Back

sin(2x) = 2sin(x)cos(x)

Front

What is the Double Angle Identity for cosine?

Back

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

Front

What is the Double Angle Identity for tangent?

Back

tan(2x) = (2tan(x)) / (1 - tan²(x))

Front

If sin x = -12/13 and tan x < 0, find sin 2x.

Back

sin(2x) = 2sin(x)cos(x) = -24/25

Front

If cos θ = 4/5 in Q IV, find sin 2θ.

Back

sin(2θ) = 2sin(θ)cos(θ) = -24/25

Front

If tan x = -12/5 and sin x > 0, find cos 2x.

Back

cos(2x) = cos²(x) - sin²(x) = -119/169

Front

If cos x = 5√34/34 and sin x < 0, find cos 2x.

Back

cos(2x) = 2cos²(x) - 1 = 8/17

Front

If cos x = 3/5 and sin x < 0, find sin 2x.

Back

sin(2x) = 2sin(x)cos(x) = -24/25

Front

What is the range of the sine function?

Back

The range of the sine function is [-1, 1].

Front

What is the range of the cosine function?

Back

The range of the cosine function is [-1, 1].