Simplify the absolute value 3|\cos ?| if ? = \sin^{−1} \frac{x}{3}

Simplify the absolute value
$3|\mathrm{cos}?|$
if
$?={\mathrm{sin}}^{-1}\frac{x}{3}$
You can still ask an expert for help

• Questions are typically answered in as fast as 30 minutes

Solve your problem for the price of one coffee

• Math expert for every subject
• Pay only if we can solve it

Nicole Conner

Step 1
Given angle is,
$0={\mathrm{sin}}^{-1}\frac{x}{3}$
Here, the objective is to find the simplify for absolute ${\mathrm{sin}}^{-1}\frac{x}{3}$.
$\mathrm{sin}0=\frac{x}{3}$
Then, by the trigonometric rule.
$\mathrm{cos}0=\sqrt{1-{\left(\frac{x}{3}\right)}^{2}}$
$=\sqrt{1-\frac{{x}^{2}}{9}}$
$=\sqrt{\frac{9-{x}^{2}}{9}}$
$=\frac{1}{3}\sqrt{9-{x}^{2}}$
Step 2
Then, the absolute value of $3|\mathrm{cos}0|$.
$3|\mathrm{cos}0|=3|\frac{1}{3}\sqrt{9-{x}^{2}}|$
$=\sqrt{9-{x}^{2}}$
Thus, this the absolute value.

Jeffrey Jordon