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Precalculus: Chapter 6 Notes: Section 6.1 Objectives: Evaluating Trigonometric Expressions Using Identities Using Law of Sines to Solve Oblique Triangles- SAS and AAS Finding Area of Oblique Triangles Applications of Law of Sines Ambiguous Case- SSA Law of Sines: sin A sin B sin C a b c EX: Use the information to solve each triangle. 1. A = 60, a = 9, b = 10 Sum and Difference Identities: 2. A = 5 degrees 40 minutes B= sin( u v) sin u cos v cos u sin v tan( u v) cos(u v) cos u cos v sin u sin v tan u tan v 1 tan u tan v EX: Find the exact value of the trigonometric function given that sin u 12 4 and cos v . (Both u 13 5 and v are in Quadrant III.) 2. cscu v 3. cotv u sin 2u 2 sin u cos u cos 2u cos 2 u sin 2 u cos 2u 2 cos 2 u 1 cos 2u 1 2 sin 2 u tan 2u 1. cosu v Double Angle Identities: 2 tan u 1 tan 2 u EX: Find the exact values of sin 2u, cos 2u, and tan 2u using the double-angle formulas. 1. cos u 4 , 5 3 u 2 2 2. cot u 3 , 2 u Half Angle Identities: sin u 1 cos u 2 2 cos u 1 cos u 2 2 tan EX: Use the figure to the right to find the exact value of the trigonometric function. 1. sin 3. sec 2 2 2. tan 2 u 1 cos u sin u 2 sin u 1 cos u