Simplifying Trig. Identities

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Presentation transcript:

Simplifying Trig. Identities Chapter5: Analytical Trigonometry “Simplify identities to sin and cos functions.”

Simplifying trig Identity Example1: simplify tanxcosx sin x cos x tanx cosx tanxcosx = sin x

Simplifying trig Identity sec x csc x Example2: simplify 1 cos x 1 cos x sinx = x sec x csc x 1 sin x = sin x cos x = tan x

Simplifying trig Identity cos2x - sin2x cos x Example2: simplify cos2x - sin2x 1 cos2x - sin2x cos x = sec x

Practice 1 cos2θ cosθ sin2θ cos2θ secθ-cosθ csc2θ cotθ tan2θ

Use pythagorean identity Example Simplify: = cot x (csc2 x - 1) Factor out cot x = cot x (cot2 x) Use pythagorean identity = cot3 x Simplify

Example Simplify: = sin x (sin x) + cos x Use quotient identity cos x Simplify fraction with LCD = sin2 x + (cos x) cos x = sin2 x + cos2x cos x Simplify numerator = 1 cos x Use pythagorean identity = sec x Use reciprocal identity

Your Turn! Combine fraction Simplify the numerator Use pythagorean identity Use Reciprocal Identity