Pythagorean Identities Unit 5F Day 2

Do Now Simplify the trigonometric expression: cot θ sin θ

Review: GCF Review: Factor out the GCF in each expression. a) a)8x – 12 b) b)3x 2 – 15x c) c)-2x 4 + 8x 2 – 10x d) d)10x x 2 e) e)-24x x 3 – 32x 2 f) f)5x – 5

Pythagorean Identities What do we get when we apply the Pythagorean theorem to a right triangle in the first quadrant of the unit circle?

Simplify the following trig. expressions. 1) 1 – sin 2 x 2) tan 2 x – sec 2 x

Simplify the following trig. expressions. 3) sin x + sin x · cot 2 x 4) sec x – sec x sin 2 x

Simplify the following trig. expressions. 6) (1 – cos x)(1 + cos x)

Verifying Trig. Identities Start with complicated side. Make it look like simple side.

Verify the following identities. 1) sin x · cot x = cos x 3) cos x · csc x = cot x

Verify the following identities. 4) sin 2 x (csc 2 x – 1) = cos 2 x 8) sin 2 x (1 + cot 2 x) = 1