Trig; Sin Problem:

**qbkr21** · November 27th 2006, 07:00 AM

Evaluate:

$sin^2x$ = $\frac{1}{2}$

$\text{Thanks!}$

**ThePerfectHacker** · November 27th 2006, 07:05 AM

Originally Posted by qbkr21

Evaluate:

$sin^2x$ = $\frac{1}{2}$

$\text{Thanks!}$

Two possibilities when you take the square root,
$\sqrt{\frac{1}{2}}=\frac{\sqrt{2}}{2}$
And,
$-\sqrt{\frac{1}{2}}=-\frac{\sqrt{2}}{2}$
Thus which (non-coterminal) angles give you this result?
$x=\pi/4,5\pi/4$

**qbkr21** · November 27th 2006, 07:08 AM

So you initially want to get $sin(x)$ by iteself? Is the method you took PerfectHacker?

**earboth** · November 27th 2006, 07:09 AM

Originally Posted by qbkr21

Evaluate:

$sin^2x$ = $\frac{1}{2}$

Hello,

$sin^2x$ = $\frac{1}{2}$ . Caculate the square-root:

$\sin(x)$ = $\frac{1}{2}\cdot \sqrt{2}$ . Now calculate arcsin:

$x = \frac{1}{4} \pi+2\pi \cdot k\ or\ x=\frac{3}{4} \pi+2\pi \cdot k$

EB

**ThePerfectHacker** · November 27th 2006, 07:10 AM

Originally Posted by qbkr21

So you initially want to get $sin(x)$ by iteself? Is the method you took PerfectHacker?

Yes.
If you want you can let,
$y=\sin x$
Then,
$y^2=\frac{1}{2}$
Thus,
$y=\pm \sqrt{\frac{1}{2}}$
Each sign is a different answer.

**qbkr21** · November 27th 2006, 07:25 AM

Thanks for the help, I clearly understand how to solve these types of problems now, however I still am unable to determine the proper notation that the computer will accept...

$sin^2(x)$ = $\frac{1}{2}$

Now it wants me to enter in just the number...
it gives me:

t= ________________ $\pi$

???? What should I do...

**qbkr21** · November 27th 2006, 10:00 AM

Here are the directions to the problem:

Give the answer as a multiple of $\pi$ . Do not use decimal numbers. The answer should be a fraction or an integer. Note that $\pi$ is already included in the answer so you just have to enter the appropriate multiple. E.g. if the answer is $\frac{\pi}{2}$ you should enter 1/2. If there is more than one answer enter them separated by commas.

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