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

• Nov 7th 2012, 05:53 PM
atpod1
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

• Nov 7th 2012, 06:06 PM
MarkFL
Re: Help with finding values of sin^2x=3/4
Take the square root of both sides, what do you find?
• Nov 7th 2012, 06:23 PM
atpod1
Re: Help with finding values of sin^2x=3/4
sin x = square root of 3/4
• Nov 7th 2012, 06:32 PM
MarkFL
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?
• Nov 7th 2012, 06:50 PM
atpod1
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
• Nov 7th 2012, 06:54 PM
MarkFL
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.
• Nov 7th 2012, 07:03 PM
atpod1
Re: Help with finding values of sin^2x=3/4
You're a genius! Thank you for your help.
• Nov 8th 2012, 12:34 AM
Petrus
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 :)