Sum and Difference Formulas

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 75o • cos 75o = cos (30o + 45o) • cos 30o cos 45o – sin 30o sin 45o

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

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

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

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

10. Finding Exact Values

11. Establishing an Identity • Establish the identity:

12. Establishing an Identity • Establish the identity • cos (a + b) + cos (a – b) = 2 cos a cos b

13. Solution • cos (a + b) + cos (a – b) = 2 cos a cos b • cos a cos b –sin a sin b + cos a cos b + sin a sin b • cos a cos b + cos a cos b = 2 cos a cos b • 2 cos a cos b = 2 cos a cos b

14. Establishing an Identity • Prove the identity: • tan (q + p) = tan q

15. Solution

16. Establishing an Identity • Prove the identity:

17. Solution

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

19. Solution • Think of this equation as the cos (a + b) (Remember that the answer to an inverse trig question is an angle). • So . . . a is in the 1st quadrant and b is in the 4th quadrant (remember range)

20. Solution

21. Solution

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

23. Solution • Let sin-1u = a and cos-1v = b • Then sin a = u and cos b = v

24. On-line Help • Tutorials • Videos