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March 10, 2017 (5.3) Sum and Difference Identities Objective: To learn the sum and difference trigonometric identities. Why: These identities provide clear examples of how different the algebra of functions can be different than the algebra of real numbers. March 10, 2017 Sum and Difference Identities Obj: To learn the sum and difference trigonometric identities. sin(u + v) = sinu cosv + cosu sinv sin(u - v) = sinu cosv - cosu sinv cos(u + v) = cosu cosv - sinu sinv cos(u - v) = cosu cosv + sinu sinv tan(u + v) = tan(u - v) = tanu + tanv 1 - tanu tanv tanu - tanv 1 + tanu tanv March 10, 2017 Obj: To learn the sum and difference trigonometric identities. Identify the sum or difference identity used. Then write the expression as the sine, cosine, or tangent of an angle. o o o 1. cos94 cos18 +sin94 sin18 2. tan 3x - tan 2y 1 + tan 3x tan 2y o March 10, 2017 Obj: To learn the sum and difference trigonometric identities. Examples. Simplify. 1. sin( π - x ) March 10, 2017 Obj: To learn the sum and difference trigonometric identities. 2. Use the sum and difference identities to prove the identity. cos( π 2 -x) = sin x March 10, 2017 Obj: To learn the sum and difference trigonometric identities. o 3. Find the exact value of sin 15 . March 10, 2017 Obj: To learn the sum and difference trigonometric identities. 7π 4. Find the exact value of cos 12 March 10, 2017 Obj: To learn the sum and difference trigonometric identities. 5π 5. Find the exact value of tan 12 March 10, 2017 HW: Obj: To learn the sum and difference trigonometric identities. Pg.425: 3, 5, 7, 23, 25, 37, 47