# Thread: Trig; Sin Problem:

1. ## Trig; Sin Problem:

Evaluate:

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

$\displaystyle \text{Thanks!}$

2. Originally Posted by qbkr21
Evaluate:

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

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

3. ## Re:

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

4. Originally Posted by qbkr21
Evaluate:

$\displaystyle sin^2x$=$\displaystyle \frac{1}{2}$
Hello,

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

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

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

EB

5. Originally Posted by qbkr21
So you initially want to get $\displaystyle sin(x)$ by iteself? Is the method you took PerfectHacker?
Yes.
If you want you can let,
$\displaystyle y=\sin x$
Then,
$\displaystyle y^2=\frac{1}{2}$
Thus,
$\displaystyle y=\pm \sqrt{\frac{1}{2}}$
Each sign is a different answer.

6. ## Re:

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...

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

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

t= ________________$\displaystyle \pi$

???? What should I do...

7. ## Re:

Here are the directions to the problem:

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