# Thread: Solve for All possible values of x: 4sin^(x)-1=0?

1. ## Solve for All possible values of x: 4sin^(x)-1=0?

I can't seem to figure the rest of this out:

Solve for All possible values of x: 4sin^2(x)-1=0?

So far I have:

Let m = sinx

So: 4m^2-1=0

How would I go about solving the rest?

2. Originally Posted by Jd09
I can't seem to figure the rest of this out:

Solve for All possible values of x: 4sin^2(x)-1=0?

So far I have:

Let m = sinx

So: 4m^2-1=0

How would I go about solving the rest?

Actually I don't really see the need for the substitution.

$\displaystyle 4sin^2x-1=0$

$\displaystyle sin^2x=1/4$

$\displaystyle sinx=1/2, -1/2$

The critical angle is pi/6. Thus if you are looking for angles between 0 and 2*pi, the possible angles are pi/6, 5*pi/6, 7*pi/6, 11*pi/6.

Hope this helps.

3. Originally Posted by Jd09
I can't seem to figure the rest of this out:

Solve for All possible values of x: 4sin^2(x)-1=0?

So far I have:

Let m = sinx

So: 4m^2-1=0

How would I go about solving the rest?

This is equivalent to $\displaystyle m^2=\frac{1}{4}\implies m=\pm\frac{1}{2}$

Since $\displaystyle m=\sin x$, then $\displaystyle \sin x=-\frac{1}{2}$ or $\displaystyle \sin x=\frac{1}{2}$.

Can you continue from here?

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### 4sin^2x-1=0

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