Thread: 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!!

Originally Posted by alexandrabel90

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, $\displaystyle Arcsin(-y) = -Arcsin(y)$

and what about for arccos?

Originally Posted by alexandrabel90

and what about for arccos?

$\displaystyle cos(t)$ is even.