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Thread: arcsin and arccos

  1. #1
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    arcsin and arccos

    why is it that arcsin(-y) = -arcsin(y) and that arccos(-y) = π (pi) - arccos(y)?

    also, what does the above 2 equations have anything to do with even and odd functions? i have no idea what is even and odd functions by the way..

    thank you!!
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  2. #2
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    Quote Originally Posted by alexandrabel90 View Post
    why is it that arcsin(-y) = -arcsin(y) and that arccos(-y) = π (pi) - arccos(y)?

    also, what does the above 2 equations have anything to do with even and odd functions? i have no idea what is even and odd functions by the way..

    thank you!!
    An even function is a function such that $\displaystyle f(-x)=f(x)$. For example, a parabola $\displaystyle y=x^2$ is an even function since: $\displaystyle f(-x)=(-x)^2=x^2=f(x)$

    An odd function is on in which $\displaystyle f(-x)=-f(x)$

    Since the sine funciton is odd, the arcsine function is also odd. Therefore, $\displaystyle Arcsin(-y) = -Arcsin(y)$
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  3. #3
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    and what about for arccos?
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  4. #4
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    Quote Originally Posted by alexandrabel90 View Post
    and what about for arccos?
    $\displaystyle cos(t)$ is even.
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