Precalculus Examples

$8 \arcsin (x) = 2 π$

Step 1

Divide each term in $8 \arcsin (x) = 2 π$ by $8$ and simplify.

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Step 1.1

Divide each term in $8 \arcsin (x) = 2 π$ by $8$ .

$\frac{8 \arcsin (x)}{8} = \frac{2 π}{8}$

Step 1.2

Simplify the left side.

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Step 1.2.1

Cancel the common factor of $8$ .

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Step 1.2.1.1

Cancel the common factor.

$\frac{8 \arcsin (x)}{8} = \frac{2 π}{8}$

Step 1.2.1.2

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

$\arcsin (x) = \frac{2 π}{8}$

Step 1.3

Simplify the right side.

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Step 1.3.1

Cancel the common factor of $2$ and $8$ .

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Step 1.3.1.1

Factor $2$ out of $2 π$ .

$\arcsin (x) = \frac{2 (π)}{8}$

Step 1.3.1.2

Cancel the common factors.

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Step 1.3.1.2.1

Factor $2$ out of $8$ .

$\arcsin (x) = \frac{2 π}{2 \cdot 4}$

Step 1.3.1.2.2

Cancel the common factor.

$\arcsin (x) = \frac{2 π}{2 \cdot 4}$

Step 1.3.1.2.3

Rewrite the expression.

$\arcsin (x) = \frac{π}{4}$

Step 2

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

$x = \sin (\frac{π}{4})$

Step 3

Simplify the right side.

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Step 3.1

The exact value of $\sin (\frac{π}{4})$ is $\frac{\sqrt{2}}{2}$ .

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

Step 4

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$x = 0.70710678 \dots$