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Thread: Trig; Sin Problem:

  1. #1
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    Trig; Sin Problem:

    Evaluate:

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


    $\displaystyle \text{Thanks!}$
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    Quote Originally Posted by qbkr21 View Post
    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?
    $\displaystyle x=\pi/4,5\pi/4$
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    Re:

    So you initially want to get $\displaystyle sin(x)$ by iteself? Is the method you took PerfectHacker?
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    Quote Originally Posted by qbkr21 View Post
    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
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    Quote Originally Posted by qbkr21 View Post
    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.
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    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...
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  7. #7
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    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.
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