1. Warm-Up: April 12, 2016
Use the sin⁡(𝛼+𝛽) formula to derive the formula for sin⁡(2𝑥)
Use the cos⁡(𝛼+𝛽) formula to derive a formula for cos⁡(2𝑥)
Use the tan (𝛼+𝛽) ⁡formula to derive a formula for tan 2𝑥

2. Homework Questions?

3. Double-Angle and Half-Angle Formulas
Section 5.3

4. Double-Angle Formulas

5. Double-Angle Derivations
8a from Identity 7a (warm-up)
8b from Identity 7c (warm-up)
8c from Identities 8b and 3a
8d from Identities 8b and 3a
8e from Identity 7e (warm-up)

6. You-Try #1
Given that sin θ = 12/13, and θ lies in quadrant II, find the exact value of:
sin 2θ
cos 2θ
tan 2θ

7. You-Try #2
Write the following expression as the sine, cosine, or tangent of a double angle. Then find the exact value.

8. Assignments Read Section 5.3 Page 573 #1-21 odd Page 573 #23-37 odd
Will be collected and checked for accuracy (not just completion)
Write clearly. Be sure to distinguish between sin 2 𝑥 and sin 2𝑥
Page 574 #39-57 odd
Page 574 #59-69 odd

11. Warm-Up: April 13/14, 2016
Given sin 𝜃 =− 3 5 and 𝜃 is in quadrant IV, calculate each of the following:

12. Homework Questions?

13. You-Try #3 – Verify the identity

14. You-Try #4 – Verify the Identity

15. You-Try #5 Solve Identity 8c for sin 2 𝑢 Solve Identity 8d for cos 2 𝑢
Divide your expressions from (a) and (b) to get an equation for tan 2 𝑢

16. Power-Reducing Identities
6a) sin 2 𝑢 = 1 2 1− cos 2𝑢 6b) cos 2 𝑢 = cos 2𝑢 6c) tan 2 𝑢 = 1− cos 2𝑢 1+ cos 2𝑢

17. You-Try #6
Rewrite 10 cos 4 𝑥 as an equivalent expression that does not contain any powers of trigonometric functions greater than one.

18. Quiz Time!!!
Clear everything off of your desk except for writing utensils and erasers.
If you appear to be talking, looking at anyone else’s quiz, allowing another student to look at your quiz, or using any unauthorized aide, you will receive a zero.
30 minute time limit

19. Quiz Question – 5th Period
Starting with any sum or difference identity, derive the other 5.
When finished, turn in your quiz to Mr. Szwast and silently work on your assignments.

20. Assignments Read Section 5.3 Page 573 #1-21 odd Page 573 #23-37 odd
Will be collected and checked for accuracy (not just completion)
Write clearly. Be sure to distinguish between sin 2 𝑥 and sin 2𝑥
Page 574 #39-57 odd
Page 574 #59-69 odd

22. Warm-Up: April 15, 2016
Given that , and θ lies in quadrant III, calculate

23. Homework Questions?

24. Half-Angle Formula Derivations
Skipping due to the minimum day.
You will not be tested on these derivations.

25. Half-Angle Formulas

26. + or - ? For 0≤𝜃<2𝜋 𝜃 in Quadrant I or II  𝜃 2 in Quadrant I
𝜃 in Quadrant III or IV  𝜃 2 in Quadrant II
Use the quadrant of 𝜃 2 to choose + or -

27. You-Try #7
Given that , and θ lies in quadrant IV, calculate:

28. Assignments Read Section 5.3 Page 573 #1-21 odd Page 573 #23-37 odd
Will be collected and checked for accuracy (not just completion)
Write clearly. Be sure to distinguish between sin 2 𝑥 and sin 2𝑥
Page 574 #39-57 odd
Page 574 #59-69 odd

29. In Exercises 39-46, use a half-angle formula to find the exact value of each expression.
In Exercises 47-54, use the figures to find the exact value of each trigonometric function. 5 3 θ 4

31. Warm-Up: April 18, 2016
Given and , calculate each of the following:

32. Homework Questions?

33. You-Try #8 – Verify the Identity

34. Assignments Read Section 5.3 Page 573 #1-21 odd Page 573 #23-37 odd
Will be collected and checked for accuracy (not just completion)
Write clearly. Be sure to distinguish between sin 2 𝑥 and sin 2𝑥
Page 574 #39-57 odd
Page 574 #59-69 odd

35. Verify Each Identity