How do you use inverse trig functions to solve equations?

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Answer 1 · 2015-04-12T05:55:26

$sinx=n$ if and only if $x=arcsinn + 2 pi k$ for some integer $k$

or $x=(pi-arcsinn) + 2 pi k$ for some integer $k$

$cosx=n$ if and only if $x=arccosn + 2 pi k$ for some integer $k$

or $x=(pi+arccosn) + 2 pi k$ for some integer $k$

$tanx=n$ if and only if $x=arctan n + pi k$ for some integer $k$

and so on.

So,: Solve $7sinx-5 = 0$

$7sinx-5 = 0$
$7sinx = 5$
$sinx = 5/7$

$x=arcsin(5/7) +2 pi k$ for integer $k$
or $(pi-arcsin(5/7)) +2 pi k$ for integer $k$