Aim: What are the double angle and half angle trig identities? Do Now: Write the identities of the following: 1. sin (A + A) 2. cos (A + A) HW: p.507 # 12,14,18 p.511 # 10,12,14

sin 2A = sin A cos A+ cos A sin A = sin A cos A + sin A cos A = 2 sin A cos A cos 2A = cos A cos A – sin A sin A = therefore, cos 2A = cos 2A = therefore,

To find the identity of tan 2A, treat 2A as A + A

Double angle identities sin 2A = 2 sin A cos A cos 2A = cos2 A – sin2 A cos 2A = 2cos2 A – 1 cos 2A = 1 – 2sin2 A

Half angle identities How do we determine when to use positive or negative ratio? It depends on the quadrant where the half angle located.

If 0 ≤ θ ≤ 90, then 0 ≤ ½ θ ≤ 45, therefore, ½ θ is on quadrant I If 180 ≤ θ ≤ 270, then 90 ≤ ½ θ ≤ 135, therefore, ½ θ is on quadrant II If 270 ≤ θ ≤ 360, then 135 ≤ ½ θ ≤ 180, therefore, ½ θ is on quadrant II

1. Show that sin 90 = 1 by using sin 2(45) sin 2(45) = 2 sin 45 cos 45 = 2. If cos A = -5/13 and A is the measure of an angle in quadrant II, find cos 2A 3. If 180 < A < 270 and find

 x is in quad I, what is the value of sin 3. If cos x = 1/9 and 3. If cos x = 1/9 and 3. If cos x = 1/9 and  x is in quad I, what is the value of sin  x is in quad I, what is the value of sin  x is in quad I, what is the value of sin Ans: 2/3 4. If sin A = – .8, what is the value of cos 2A? Ans: – .28 5. If A = , what is the value of sin Ans: 2/5 6. If cos x = -3/5 and sin x < 0, find the value of sin 2x Ans: 24/25