SOLUTION: find all exact solutions to the equation on [0,2 pi): 2 sin^2u= 1-sinu

Question 775359: find all exact solutions to the equation on [0,2 pi): 2 sin^2u= 1-sinu
Answer by htmentor(1343) (Show Source): You can put this solution on YOUR website!
First move all the terms to LHS:
2sin^2(u) + sin(u) - 1 = 0
If we let x=sin(u), this gives
2x^2 + x - 1 = 0
This can be factored as (2x-1)(x+1) = 0
This gives x = 1/2, x = -1, or sin(u) = 1/2, sin(u) = -1
(Or we could have completed the factoring in terms of sin(u) directly)
I'll leave it as an exercise for you to determine the values of u.

RELATED QUESTIONS
Find the exact values of sin 2u , Cos 2u, and tan 2u using double angle formulas. 1.... (answered by stanbon)

Find all solutions to the equation in the interval (0,2pi).... (answered by KMST,tommyt3rd)

Please help me solve this equation use a double angle formulas to find the exact value... (answered by lwsshak3)

Find the exact values of sin(2u), cos(2u), and tan(2u) using the double-angle formulas.... (answered by lwsshak3)

Find the exact values of sin(2u), cos(2u), and tan(2u) using the double-angle formulas. (answered by Boreal,MathTherapy,Alan3354)

Find all solutions to the equation sin x = 0. a. x = {{{PI}}}n b. x = 2{{{PI}}}n c. x... (answered by bucky)

Find all exact solutions on (0, 2pi) sec(x) sin(x) - 2 sin(x) =... (answered by Boreal,MathLover1)

Use a double-angle formula to find the exact value of cos(2u) when sin(u)=8/17, where... (answered by ewatrrr)

Find all solutions in the interval [0,2PI] to the equation {{{cos^(2)(x=1)}}}. a. x = 0, (answered by jim_thompson5910,ffc_01)