simplifying trigonometric identities

What is the Pythagorean identity for sine and cosine?

sin²(θ) + cos²(θ) = 1.

How do you simplify sin(-θ)?

sin(-θ) = -sin(θ).

What is the value of tan(θ) in terms of sine and cosine?

tan(θ) = sin(θ) / cos(θ).

What is the reciprocal identity for cosecant?

csc(θ) = 1/sin(θ).

What is the identity for secant in terms of cosine?

sec(θ) = 1/cos(θ).

How do you simplify cos(θ + π)?

cos(θ + π) = -cos(θ).

What is the angle sum identity for sine?

sin(α + β) = sin(α)cos(β) + cos(α)sin(β).

How do you express cotangent in terms of sine and cosine?

cot(θ) = cos(θ) / sin(θ).

What is the double angle formula for sine?

sin(2θ) = 2sin(θ)cos(θ).

How do you simplify cos(-θ)?

cos(-θ) = cos(θ).