# Calculus

I need to find the exact solutions on the interval [0,2pi) for:
2sin^2(x/2) - 3sin(x/2) + 1 = 0

I would start:
(2sin(x/2)-1)(sin(x/2)-1) = 0
sin(x/2)=1/2 and sin(x/2)=1

what's next?

Ok, what angle has a sin equal to say 1/2
sin (x/2)=1
arc sin (1) = x/2
PI/2=x/2
solve for x
do the same technique for the other solution.

so the solution is pi and the other solution would be
arc sin (1/2) = x/2
pi/6 = x/2
x= pi/3
is that right?

1. 👍 0
2. 👎 0
3. 👁 170

## Similar Questions

1. ### trig

I need to find all solutions of the given equations for the indicated interval. Round solutions to three decimal places if necessary. 1.) 3sin(x)+1=0, x within [0,2pi) 2.) 2sin(sq'd)(x)+cos(x)-1=0, x within R 3.)

asked by Emily on June 21, 2009
2. ### Math

Can I please get some help on these questions: 1. How many solutions does the equation,2sin^2 2 θ = sin2θ have on the interval [0, 2pi]? 4? ...what about 4cos2θ = 8cos^2 2θ? 2. True or False: sin^2 4x = 1 has 8 solutions on

asked by mysterychicken on June 2, 2013
3. ### math

Find all solutions to the equation tan(t)=1/tan (t) in the interval 0

asked by alicia otto on March 26, 2016
4. ### Mathematics

Given that 2cos^2 x - 3sin x -3 = 0, show that 2sin^2 x + 3sin x +1 = 0? Hence solve 2cos^2 x + 4sin x - 3 = 0, giving all solutions in the interval 0 ≤ x ≤ 2π

asked by Sean on November 18, 2015
5. ### trig

2sin(x)cos(x)+cos(x)=0 I'm looking for exact value solutions in [0, 3π] So I need to find general solutions to solve the equation. But do I eliminate cos(x), like this... 2sin(x)cos(x)+cos(x)=0 2sin(x)cos(x)= -cos(x) 2sin(x) = -1

asked by Alex on March 23, 2008
6. ### Precalculus

2sin^2x+3cosx=3 find all solutions in the interval [0,2pi]

asked by Megan on December 8, 2010
7. ### trig

Find all solutions of the equation 2sin^2x-cosx=1 in the interval [0,2pi) x1= ? x2=? x3=?

asked by Natash on November 22, 2008
8. ### Math

8. Solve each of the following trigonometric equations and find all solutions in the interval: 0

asked by !! on February 23, 2019
9. ### Math Trig

Find all solutions on the interval [0,2pi] for the following: 2sin^2(x)-5sin(x)=-3 cos^2(x)+sin(x)=1

asked by Kelly on March 14, 2011
10. ### College Pre-Algegra

1. Find the exact value of tan660 using the functions of 330deg. 2. Solve the equation 2sin^20+5sin0+3=0 on the interval 0

asked by clifford on June 12, 2011

More Similar Questions