How do you simplify $cos (arcsin (\frac{x}{3}))$ $Cos( arcsin (x/3))$ ?

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Answer 1 · 2016-07-28T13:53:32

$\sqrt{1 - \frac{x^{2}}{9}}$ $sqrt(1-x^2/9)$

Let $a = a r c sin (\frac{x}{3})$ $a = arc sin (x/3)$ is in Q1 or Q4..

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

The given expression is cos a.

Answer 2 · 2016-07-28T14:04:37

$cos [arcsin (\frac{x}{3})] = \frac{\sqrt{9 - x^{2}}}{3} \to \sqrt{1 - \frac{x^{2}}{9}}$ $cos[arcsin(x/3)]=sqrt(9-x^2)/3" "->" "sqrt(1-x^2/9)$

$arcsin (\frac{x}{3})$ $arcsin(x/3)$ returns the angle $θ$ $theta$

Tony B
$\Rightarrow cos (θ) = \frac{\sqrt{9 - x^{2}}}{3}$ $=>cos(theta)= sqrt(9-x^2)/3$

$\Rightarrow cos (arcsin (\frac{x}{3})) = \frac{\sqrt{9 - x^{2}}}{3}$ $=>cos(arcsin(x/3))=sqrt(9-x^2)/3$

How do you simplify cos(arcsin(x3))Cos( arcsin (x/3))?