1. Sum and Difference Formulas New Identities

2. Cosine Formulas

3. Sine Formulas

4. Tangent Formulas

5. Using Sum Formulas to Find Exact Values Find the exact value of cos 75 o Find the exact value of cos 75 o cos 75 o = cos (30 o + 45 o ) cos 75 o = cos (30 o + 45 o ) cos 30 o cos 45 o – sin 30 o sin 45 o cos 30 o cos 45 o – sin 30 o sin 45 o

6. Find the Exact Value Find the exact value of Find the exact value of

7. Exact Value Find the exact value of tan 195 o Find the exact value of tan 195 o

8. Using Difference Formula to Find Exact Values Find the exact value of Find the exact value of sin 80 o cos 20 o – sin 20 o cos 80 o sin 80 o cos 20 o – sin 20 o cos 80 o This is the sin difference identity so... This is the sin difference identity so... sin(80 o – 20 o ) = sin (60 o ) = sin(80 o – 20 o ) = sin (60 o ) =

9. Using Difference Formula to Find Exact Values Find the exact value of Find the exact value of cos 70 o cos 20 o – sin 70 o sin 20 o cos 70 o cos 20 o – sin 70 o sin 20 o This is just the cos difference formula This is just the cos difference formula cos (70 o + 20 o ) = cos (90 o ) = 0 cos (70 o + 20 o ) = cos (90 o ) = 0

10. Finding Exact Values

11. Establishing an Identity Establish the identity: Establish the identity:

12. Establishing an Identity Establish the identity Establish the identity cos (  cos (  –  cos  cos  cos (  cos (  –  cos  cos 

13. Solution cos  cos  –  sin  sin  + cos  cos  sin  sin  cos  cos  –  sin  sin  + cos  cos  sin  sin  cos  cos  cos  cos  cos  cos  cos  cos  cos  cos  cos  cos   cos  cos  =  cos  cos   cos  cos  =  cos  cos 

14. Establishing an Identity Prove the identity: Prove the identity: tan (  = tan  tan (  = tan 

15. Solution

16. Establishing an Identity Prove the identity: Prove the identity:

17. Solution

18. Finding Exact Values Involving Inverse Trig Functions Find the exact value of: Find the exact value of:

19. Solution Think of this equation as the cos (   Remember that the answer to an inverse trig question is an angle). Think of this equation as the cos (   Remember that the answer to an inverse trig question is an angle). So...  is in the 1 st quadrant and  is in the 4 th quadrant (remember range) So...  is in the 1 st quadrant and  is in the 4 th quadrant (remember range)

20. Solution

21. Solution

22. Writing a Trig Expression as an Algebraic Expression Write sin (sin -1 u + cos -1 v) as an algebraic expression containing u and v (without any trigonometric functions) Write sin (sin -1 u + cos -1 v) as an algebraic expression containing u and v (without any trigonometric functions) Again, remember that this is just a sum formula Again, remember that this is just a sum formula sin (  = sin  cos  + sin  cos  sin (  = sin  cos  + sin  cos 

23. Solution Let sin -1 u =  and cos -1 v =  Let sin -1 u =  and cos -1 v =  Then sin  u and cos  = v Then sin  u and cos  = v

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