How do you simplify $Cos( arcsin (x/3))$ ?

Question

11874 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-07-28T13:53:32

$sqrt(1-x^2/9)$

Let $a = arc sin (x/3)$ is in Q1 or Q4..

Then, $sin a = x/3 and cos a = sqrt(1-x^2/9) >= 0$ , in Q1 and Q4.

The given expression is cos a.

Answer 2 · 2016-07-28T14:04:37

$cos[arcsin(x/3)]=sqrt(9-x^2)/3" "->" "sqrt(1-x^2/9)$

$arcsin(x/3)$ returns the angle $theta$

Tony B Tony B
$=>cos(theta)= sqrt(9-x^2)/3$

$=>cos(arcsin(x/3))=sqrt(9-x^2)/3$

How do you simplify Cos( arcsin (x/3))Cos( arcsin (x/3))?