How do you simplify $cos(arcsin(1/3))$ ?

Question

3924 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-02-04T06:30:24

$cos(arcsin(1/3))=(2sqrt2)/3$

$arcsinx$ is the angle $theta$ for which $sintheta=1/3$

or $theta=arcsin(1/3)$

As $sintheta=1/3$ , $costheta=sqrt(1-(1/3)^2)=sqrt(8/9)=(2sqrt2)/3$

Now as $costheta=(2sqrt2)/3$ and $theta=arcsin(1/3)$

$cos(arcsin(1/3))=(2sqrt2)/3$

How do you simplify cos(arcsin(1/3))cos(arcsin(1/3))?