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

Homework Questions?

Double-Angle and Half-Angle Formulas Section 5.3

Double-Angle Formulas

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)

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

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

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

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

Homework Questions?

You-Try #3 – Verify the identity

You-Try #4 – Verify the Identity

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

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

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

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

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.

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

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

Homework Questions?

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

Half-Angle Formulas

+ 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 -

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

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

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

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

Homework Questions?

You-Try #8 – Verify the Identity

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

Verify Each Identity