Warm-up: Find sin(195o) HW : pg. 501(1 – 18).

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Presentation transcript:

Warm-up: Find sin(195o) HW : pg. 501(1 – 18)

HW Answers: pg. 490(1 – 4, 7 – 16, 21- 24, 45 – 48)

Ch 5.5: Double – Angle Formulas Objective: Use Double – Angle Formulas

Double Angle Formulas

Solving a Trigonometric Equation Find all the solutions of 2 cosx + sin 2x = 0 2 cosx + sin 2x = 0 2 cosx + 2sinxcosx = 0 2 cosx(1 + sinx) = 0 cosx = 0, 1 + sinx = 0    

Evaluating Functions Involving Double Angles Ex: Find the sin2Ө, cos2Ө, and tan2Ө if

Find sin(x + y), cos(x + y) and tan(x + y) given sinx = 12/13, cosx < 0 siny = -4/5 , 3π/2 < y < 2π 3 13 12 -4 5 -5 Sin(x + y) = sinxcosy + cosxsiny     cos(x + y) = cosxcosy – sinxsiny  

Find sin2x and cos2y given sinx = -15/17, π < x < 3π/2 siny = 4/5 , cosy < 0 -8 5 4 -15 17 -3

Solve 2cos(2x) + 2sin2x = 1 for [0, 2)

Sneedlegrit: Find sin(15o) HW : pg. 501(1 – 18)