1. Section 10.4: Sum and Difference Formulas If I asked you to find an exact value of trigonometric function without a calculator, which angles could you use?

3. The sum and difference formulas allow you to add or subtract any two of the special angles found on our unit circle WITHOUT a calculator.

4. sin (u ± v) = sin u cos v ± cos u sin v (same sign) cos (u ± v) = cos u cos v ∓ sin u sin v (opposite sign)

5. Ex. 1 Find the exact value of cos 75 (Ask yourself... how can I use the special angles from my unit circle to add or subtract and yield 75?) How about 45 + 30 ?

6. cos 75 = cos 45 cos 30 - sin 45 sin 30

7. (Ask yourself...how can I use the special angles from my unit circle to add or subtract and yield π/12? I know this involves fractions, but they are my friend.) Tip: This problem is in 12ths. So, look at the angles on your unit circle in terms of 12ths versus their reduced form. Ex. 2. Find the exact value of the sin π 12.

8. How about π 3 - π 4 ? sin π 12 =

9. Find the exact value of Ex. 3: Let’s Try A Tangent Problem!

11. Ex. 4: Let’s go backward! Find the exact value of:

12. 10.4 Learning Opportunity Read Section 10.4 p. 653 #1-35 odd

13. 10.5 Double and Half Angle Formulas In this section, we will continue to add to our identities. So far we have learned: Reciprocal Identities Quotient Identities Pythagorean Identities Cofunction Identities Even/Odd Identities Sum and Difference Identities

14. Double Angle Formulas

15. The sign depends on the quadrant where θ/2 is located

16. Ex. 1 Use the following to find sin 2θ, cos 2θ, tan 2θ

17. Ex. 2 Use the following to find:

18. Ex. 3 Use the figure to find the exact value of the trigonometric function. 4 1 θ a.tan θ b.sin 2θ c.sec 2θ d.cot 2θ

19. Ex. 4 Use the figure to find the exact value of the trigonometric function. 15 8 θ

20. 10.5 Learning Opportunity Please Read Section 10.5 p. 660-661 #1-7 odd, 23-27 odd, 35-39 odd, 49-53 odd