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Aim: What are the double angle and half angle trig identities?

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: Worksheet.

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Aim: What are the double angle and half angle trig identities?

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  1. 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: Worksheet

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

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

  4. Double angle identities • sin 2A = 2 sin A cos A • cos 2A = cos2 A – sin2A • cos 2A = 2cos2A – 1 • cos 2A = 1 – 2sin2A

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

  6. If 0 ≤ θ ≤ 90, then 0 ≤ ½ θ≤ 45, therefore,½ θis on quadrant I If 90 ≤ θ ≤ 180, then 45 ≤ ½ θ ≤ 90, 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

  7. 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

  8. 3. If cos x = 1/9and 3. If cos x = 1/9and 3. If cos x = 1/9and  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

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