# Math Help - Help with finding values of sin^2x=3/4

1. ## Help with finding values of sin^2x=3/4

x should be theta but I don't where the theta symbol is.

I need to find all the values of x, 0<=x<=2Pi for:

sin2x=3/4

2. ## Re: Help with finding values of sin^2x=3/4

Take the square root of both sides, what do you find?

3. ## Re: Help with finding values of sin^2x=3/4

sin x = square root of 3/4

4. ## Re: Help with finding values of sin^2x=3/4

Don't forget the $\pm$ when you take the square root. So you have:

$\sin(x)=\pm\frac{\sqrt{3}}{2}$

You will have 4 solutions on the given interval...can you find them?

5. ## Re: Help with finding values of sin^2x=3/4

I see. The square root of 3/4 is, square root 3/2, which is Pi/3

Therefore as it is Positive in quadrants I and II the angle must be Pi - Pi/3 = 2Pi/3

so for + square root 3/2 the angles are Pi/3 and 2Pi/3

and for - square root 3/2 the angles are 4Pi/3 and 5Pi/3

6. ## Re: Help with finding values of sin^2x=3/4

Yes, good work!

You found the quadrant I solution, then used the identity $\sin(\pi-x)=\sin(x)$ to get the quadrant II solution, then used the identity $-\sin(x)=\sin(-x)$ along with $\sin(x+2\pi)=\sin(x)$ to get the quadrant III and IV solutions.

7. ## Re: Help with finding values of sin^2x=3/4

You're a genius! Thank you for your help.

8. ## Re: Help with finding values of sin^2x=3/4

just think like normal equation when u solve sin,tan and cos the only diffrent is kinda you have to take away or add pi to get to your intervall :P. Took me so long time to understand this and its so simple (I feel stupid that i did not understand this alot early <.<) btw i recomend to always draw unit circle