SOLUTION: Determine all solutions , in radian measure , for the equation: {{{sin(expr(1/2)(theta - pi/3)^"")}}}{{{""=""}}}{{{-sqrt(3)/2}}}

Algebra ->  Trigonometry-basics -> SOLUTION: Determine all solutions , in radian measure , for the equation: {{{sin(expr(1/2)(theta - pi/3)^"")}}}{{{""=""}}}{{{-sqrt(3)/2}}}       Log On


   



Question 1181526: Determine all solutions , in radian measure , for the equation:
sin%28expr%281%2F2%29%28theta+-+pi%2F3%29%5E%22%22%29%22%22=%22%22-sqrt%283%29%2F2

Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
sin%28expr%281%2F2%29%28theta+-+pi%2F3%29%5E%22%22%29%22%22=%22%22-sqrt%283%29%2F2

The sine is negative in QIII and QIV, so

expr%281%2F2%29%28theta+-+pi%2F3%29%22%22=%22%22matrix%281%2C3%2C4pi%2F3%2B2pi%2An%2Cor%2C5pi%2F3%2B2pi%2An%29

Multiply through by 2

theta+-+pi%2F3%22%22=%22%22matrix%281%2C3%2C8pi%2F3%2B4pi%2An%2Cor%2C10pi%2F3%2B4pi%2An%29

Add pi/3 to both sides

theta%22%22=%22%22matrix%281%2C3%2C9pi%2F3%2B4pi%2An%2Cor%2C11pi%2F3%2B4pi%2An%29

theta%22%22=%22%22matrix%281%2C3%2C3pi%2B4pi%2An%2Cor%2C11pi%2F3%2B4pi%2An%29

factor out π:

theta%22%22=%22%22matrix%281%2C3%2Cpi%2A%283%2B4n%29%2Cor%2Cpi%2A%2811%2F3%2B4n%29%29

Edwin