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Name ____________________________________Date ______________Block _____ Adv. Math: Chapter 5 Lesson 2: Trigonometric Ratios in Right Triangles Objectives: Find the values of trigonometric ratios for acute angles of right triangles Acute: Complementary: B C A Trigonometric Ratios: Trig. Ratios Words Symbol Definition sine Θ sin Θ sin Θ = _________________ cosine Θ cos Θ cos Θ = _________________ tangent Θ tan Θ tan Θ = _________________ **Mnemonic Device . . . . Ex. 1: a) Find the values of the sine, cosine, and tangent for < B. C B 18m 33m A b) Find the values of the sine, cosine, and tangent for < A. C 8cm B Reciprocal Trig. Ratios 15cm Words Symbol Definition cosecant Θ csc Θ csc Θ = _____or ________________ secant Θ sec Θ sec Θ = ______or _______________ cotangent Θ cot Θ cot Θ = _____or ________________ **Reciprocal Identities** A Ex. 3: a) If cos Θ = ¾ , find sec Θ. c) b) If sin Θ = 0.8, find csc Θ. If csc Θ = 1.345, find sin Θ. Ex. 4: a) Find the values of the six trig. ratios for < P. P 10 cm M 7 cm N D b) Find the values of the six trig. ratios for < E. 3 cm E 7 cm F Special Triangles: 30-60-90 and Θ sin Θ cos Θ 45-45-90 tan Θ csc Θ sec Θ cot Θ 30 45 60 Cofunctions - sin Θ = cos (90-Θ) tan Θ = cot (90-Θ) sec Θ = csc (90-Θ) HOMEWORK: cos Θ = sin (90-Θ) cot Θ = tan (90-Θ) csc Θ = sec (90-Θ)