Today we will be learning: -How to evaluate trigonometric functions - PowerPoint PPT Presentation

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 Cos  = adj/hyp Side Tan  = opp/adj  Adjacent Side 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.) 13 Hyp = 5  12 5 13 csc  = sin  = 13 12 5 13 sec  = cos  = 12 13 5 12 cot  = tan  = 12 5

1 2 2  sin 45º = 2 45º 2 1 2 1 2  cos 45º = 2 1 45º tan 45º = 1

1 sin 30º = sin  /6 = 2 30º 2 3 cos 30º = cos  /6 = 3 2 1 3 tan 30º = tan  /6 = 3  3 60º 3 sin 60º = sin  /3 = 1 2 1 cos 60º = cos  /3 = 2 tan 60º = tan  /3 = 3

Co-functions of complementary angles are equal. 1 sin 30º = = cos 60 º 2 3 cos 30º = = sin 60 º 2 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. 5  3 2.5  sin  = 1.5 1.5/2.5 = 3/5 4 2.0 cos  = 2.0/2.5 = 4/5 sin  = 3/5 cos  = tan  = 4/5 3/4 tan  = 3/4 csc  = csc  = 5/3 5/3 sec  = 5/4 cot  = 4/3 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  . 4 3 A. sin  = 3/4  7 cos  = √7 4 4 csc  = 3 7 cot  =  3 7 3 3 tan  = 7 7 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 √1 3 B. cot  = 3/2 2  2 13  2 13 sin  = 3 13 2 tan  = 3 3 13  3 13 cos  = 13 csc  = 13 2 13 sec  = 3 Homework: p. 156 #2-16 even