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

 Adjacent Side Opposite Side Sin  = opp/hyp Cos  = adj/hyp Tan  = opp/adj Csc  = hyp/opp Sec  = hyp/adj Cot  = adj/opp

SOH CAH TOA

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.)

5 12

 Hyp =

sin  = cos  = tan  =

13

csc  = sec  = cot  =

5 13 12 13 5 12 13 5 13 12 12 5

45º 45º

1 1 sin 45º = cos 45º = tan 45º =

2

1 2  2 2 1 2  2 2

1

sin 30º = sin /6 = cos 30º = cos /6 = tan 30º = tan /6 =

1

2

30º 60º

sin 60º = sin /3 = cos 60º = cos /3 = tan 60º = tan /3 =

3

1 2 3 2

1 3 

3 3 3 2 1 2

3

Co-functions of complementary angles are equal.

sin 30º = = cos 60 º cos 30º = = sin 60 º sin & cos tan & cot csc & sec Co-function Pairs

3 2

1 2

Ex 2: Find the exact values of the six Trig functions of the angle  for each of the two triangles. sin  = cos  = tan  = csc  = sec  = cot  = sin  = cos  = tan  = csc  = sec  = cot  = 3 5  2.5  1.5 3/5 1.5/2.5 = 3/5

4 2.0

4/5 2.0/2.5 = 4/5 3/4 3/4 5/3 5/3 5/4 5/4 4/3 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  = tan  =



3 4 √7

csc  = sec  =

7 4 3 7  3 7 7

cot  =

4 3

 4 7 7 4 7 7 3

Homework: p. 156 #2-16 even

• B. cot  = 3/2

sin  = cos  =

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 .

tan  = csc  = sec  = 

adj/opp

3 2 √13

2 13 2 13 13 3 13  3 13 13

2 3

13 2 13 3