SOLUTION: Solve the following equation for all radian solutions and if 0 &#8804; x < 2&#960;. Give all answers as exact values in radians. Do not use a calculator. (Enter your answers as

Algebra ->  Trigonometry-basics -> SOLUTION: Solve the following equation for all radian solutions and if 0 &#8804; x < 2&#960;. Give all answers as exact values in radians. Do not use a calculator. (Enter your answers as      Log On


   

Question 858565: Solve the following equation for all radian solutions and if
0 ≤ x < 2π.
Give all answers as exact values in radians. Do not use a calculator. (Enter your answers as a comma-separated list. If there is no solution, enter NO SOLUTION.)
2 sin2 x + sin x − 1 = 0
(b) 0 ≤ x < 2π
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Substitute, u=sin%28x%29
2u%5E2%2Bu-1=0
%28u%2B1%29%282u-1%29=0
Two solutions:
u%2B1=0
u=-1
sin%28x%29=-1
x=%283pi%29%2F2
and
2u-1=0
2u=1
u=1%2F2
sin%28x%29=1%2F2
x=pi%2F6 and x=%285pi%29%2F6