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Today we will be learning: -How to evaluate trigonometric functions of acute angles. -How to use the fundamental trigonometric identities. Lesson 1.3 Rt. Trigonometry Sin = opp/hyp Opposite Side Adjacent Side Cos = adj/hyp Tan = opp/adj Csc = hyp/opp Sec = hyp/adj SOH CAH TOA Cot = adj/opp Ex 1: Find the exact values of the six Trig functions of the angle shown in the figure. (Use the Pythagorean Theorem to find the third side of the triangle.) Hyp = 13 5 5 sin = 13 cos = 5 tan = 12 12 12 13 13 csc = 5 sec = 12 cot = 5 13 12 1 2 sin 45º = 2 2 45º 2 1 45º 1 2 cos 45º = 2 2 tan 45º = 1 1 1 sin 30º = sin /6 = 2 30º 2 60º 1 3 cos 30º = cos /6 = 3 2 1 3 tan 30º = tan /6 = 3 3 3 sin 60º = sin /3 = 2 1 cos 60º = cos /3 = 2 tan 60º = tan /3 = 3 Co-functions of complementary angles are equal. sin 30º = 1 2 = cos 60 º cos 30º = 3 2 = sin 60 º Co-function Pairs sin & cos tan & cot csc & sec Ex 2: Find the exact values of the six Trig functions of the angle for each of the two triangles. 3 5 4 sin = 3/5 cos = 4/5 tan = 3/4 csc = 5/3 sec = 5/4 cot = 4/3 1.5 2.5 sin = 1.5/2.5 = 3/5 2.0 cos = 2.0/2.5 = 4/5 tan = 3/4 csc = 5/3 sec = 5/4 cot = 4/3 Ex 3: Sketch a right triangle corresponding to the trig function of the acute angle . Use the Pyth. Thm. to determine the third side, then find the other five trig functions of . A. sin = 3/4 cos = 7 4 3 3 7 tan = 7 7 4 3 4 csc = 3 √7 7 cot = 3 4 4 7 sec = 7 7 Ex 3(cont’d): Sketch a right triangle corresponding to the trig function of the acute angle . Use the Pyth. Thm. to determine the third side, then find the other five trig functions of . adj/opp B. cot = 3/2 2 2 13 sin = 13 13 cos = 3 3 13 13 13 Homework: p. 156 #2-16 even √13 2 2 tan = 3 csc = sec = 3 13 2 13 3