1. 5-4 Multiple-Angle Identities

2. Trig Identities Song To the tune of Rudolph the Red-Nosed Reindeer You know reciprocal and quotient and cofunction and odd/even We’ve also done the sum or the difference and pythagorean But do you recall the most challenging identities of all? First we have double angle, don’t forget that cosine has 3, Next are the power-reducing, you need time to memorize these. Lastly are the half angle, these all involve a square root – The sheet Mrs. Mullen just gave you should help you do these proofs. It’s almost time for Christmas Eve, things will get easier by then – We’ll do Laws of Sines and Cosines, finish with limits. The end! I challenge you to keep trying… these lovely trig identities They’ll help you be problem solvers and maybe YOU’LL go down in history!

3. Recall sums & differences cos (  ) = cos  cos   sin  sin  sin (  ) = sin  cos   cos  sin  tan (   ) = tan   tan  1  tan  tan 

4. Group Work – Sine of a Double Angle Using the sine of a sum formula, substitute in , for both angles Simplify the results What is a formula for sin (  +  ) of sin 2  ?

5. Sine of a Double Angle Identity Sin 2  = 2sin  cos  Ex 1 Write the expression as one involving only sin  and cos  : sin 2  + cos 

6. Group Work – Cosine of a Double Angle Using the cosine of a sum formula, substitute in , for both angles Simplify the results What is a formula for cos (  +  ) of cos 2  ? Using the Pythagorean theorem identities for cos 2  and sin 2 , find two other formulas for cos 2 

7. Cosine of a Double Identity cos 2  = cos 2  sin 2   = 2cos 2  1 = 1 – 2sin 2  Ex 2 Find all the solutions to the equation: cos 2x = cos x

8. Group Work – Tangent of a Double Angle Using the tangent of a sum formula, substitute in , for both angles Simplify the results What is a formula for tan (  +  ) of tan 2  ?

9. Tangent of a Double Angle Identity tan 2  = 2tan  1 – tan 2  Ex 3 Prove 2csc 2u = csc 2 u tan u

10. Ex 4 Prove the identity a) cos 6x = 2cos 2 (3x) – 1 b) sin 4x = 2 sin2x cos2x

11. Ex 5 Solve algebraically for exact solutions in the interval [0,2  ). Use your calculator to support your work. a) cos 2x + cos x = 0 b) sin 2x – cos 3x = 0 c) cos 2x = sin x

12. Exit Ticket Write the expression as one involving only sin  and cos  :sin 3  + cos 2 

13. Tonight’s Assignment P. 475 Ex 6 - 30 m. of 3 Study for Unit # 8 Test on Sums, Differences and Multiple Angles