Precalculus Examples

$30 \arcsin (x) = 5 π$

Step 1

Divide each term in $30 \arcsin (x) = 5 π$ by $30$ and simplify.

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Step 1.1

Divide each term in $30 \arcsin (x) = 5 π$ by $30$ .

$\frac{30 \arcsin (x)}{30} = \frac{5 π}{30}$

Step 1.2

Simplify the left side.

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Step 1.2.1

Cancel the common factor of $30$ .

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Step 1.2.1.1

Cancel the common factor.

$\frac{30 \arcsin (x)}{30} = \frac{5 π}{30}$

Step 1.2.1.2

Divide $\arcsin (x)$ by $1$ .

$\arcsin (x) = \frac{5 π}{30}$

Step 1.3

Simplify the right side.

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Step 1.3.1

Cancel the common factor of $5$ and $30$ .

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Step 1.3.1.1

Factor $5$ out of $5 π$ .

$\arcsin (x) = \frac{5 (π)}{30}$

Step 1.3.1.2

Cancel the common factors.

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Step 1.3.1.2.1

Factor $5$ out of $30$ .

$\arcsin (x) = \frac{5 π}{5 \cdot 6}$

Step 1.3.1.2.2

Cancel the common factor.

$\arcsin (x) = \frac{5 π}{5 \cdot 6}$

Step 1.3.1.2.3

Rewrite the expression.

$\arcsin (x) = \frac{π}{6}$

Step 2

Take the inverse arcsine of both sides of the equation to extract $x$ from inside the arcsine.

$x = \sin (\frac{π}{6})$

Step 3

Simplify the right side.

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Step 3.1

The exact value of $\sin (\frac{π}{6})$ is $\frac{1}{2}$ .

$x = \frac{1}{2}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{1}{2}$

Decimal Form:

$x = 0.5$