Use doubleangle identities to solve the equation Find all so

Use double-angle identities to solve the equation. Find all solutions over the interval [0, 2]. (Enter your answers as a comma-separated list. Find exact values when possible; if not possible, round your answers to four decimal places.)

6 sin()cos() = 0.5

Solution

-6sincos = 0.5

sincos = -0.5/6 = -0.0833

2sincos = -0.167

sin2 = -0.167

2 = sin^-1(-0.167)

2 = 2pi - 0.167 = 6.1162

2 = 2k*pi +6.112

= (2k*pi +6.112)/2

= 3.0581 , 6.1996 (rad)

2 = pi +0.167

2 = 2k*pi + 3.3086

= (2k*pi + 3.3086)/2

= 1.6543 , 4.7959