1. 6.2.2 The Trigonometric Functions

2. The Functions Squared sin 2 (  ) = sin(  ) 2 = sin(  ) * sin(  ) sin 2 (  ≠ sin (  2 ) = sin (  *  )

3. The Fundamental Identities Reciprocal Identities: The tangent and cotangent identities: The Pythagorean Identities:

4. sin 2 (  ) + cos 2 (  ) = 1 What happens if you divide by sin 2 (  )? What happens if you divide by cos 2 (  )? Use the tangent and cotangent identities

5. Uses: sin 2 (  ) + cos 2 (  ) = 1 sin(  ) = sqrt( 1 - cos 2 (  )) and cos(  ) = sqrt(1 - sin 2 (  ) ) tan(  ) = sin(  )/cos(  ) = sin(  )/ (sqrt(1 - sin 2 (  ) ))

6. New way to look at an angle, angles in standard position Sin (  ) = y/r Cos (  ) = x/r Tan (  ) = y/x  O P(x,y) Q(x,0) X r (h) Y x y All 6 functions are defined so long as x,y ≠ 0 Sine and cosine are defined for all angles (Unit Circle)

7. Ex1)  O P(15,8)r (h) x y r 2 = 15 2 + 8 2 = 225 + 64 = 289 = 17 2 r = 17 Sin = 15/17; cos = 8/17 tan = 8/15

8. Ti-83 Calculator Make sure you are in the right mode! Radian mode Degree mode Problems 27 and 29 require a calculator, table of values, or computer program to estimate

9. Using Identity properties 32) csc 2 (3a) – cot 2 (3a) = (1/ sin 2 (3a)) – (cos 2 (3a)/ sin 2 (3a)) = (1 – cos 2 (3a) )/ (sin 2 (3a)) sin 2 (3a)/sin 2 (3a) = 1

10. simplify 36) cot 2 (a) – 4 / (cot 2 (a) – cot (a) – 6) = (Cot (a) – 2) (cot (a) + 2) / ((cot(a) – 3)(cot(a) + 2) = cot(a) – 2 / cot(a) - 3

11. Homework P. 418 27- 35 odd, 38, 39 – 51 odd, 57, 67, 71