Trigonometry Examples

$2 \arcsin (x) = \frac{π}{3}$

Step 1

Divide each term in $2 \arcsin (x) = \frac{π}{3}$ by $2$ and simplify.

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Step 1.1

Divide each term in $2 \arcsin (x) = \frac{π}{3}$ by $2$ .

$\frac{2 \arcsin (x)}{2} = \frac{\frac{π}{3}}{2}$

Step 1.2

Simplify the left side.

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Step 1.2.1

Cancel the common factor of $2$ .

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Step 1.2.1.1

Cancel the common factor.

$\frac{2 \arcsin (x)}{2} = \frac{\frac{π}{3}}{2}$

Step 1.2.1.2

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

$\arcsin (x) = \frac{\frac{π}{3}}{2}$

Step 1.3

Simplify the right side.

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Step 1.3.1

Multiply the numerator by the reciprocal of the denominator.

$\arcsin (x) = \frac{π}{3} \cdot \frac{1}{2}$

Step 1.3.2

Multiply $\frac{π}{3} \cdot \frac{1}{2}$ .

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Step 1.3.2.1

Multiply $\frac{π}{3}$ by $\frac{1}{2}$ .

$\arcsin (x) = \frac{π}{3 \cdot 2}$

Step 1.3.2.2

Multiply $3$ by $2$ .

$\arcsin (x) = \frac{π}{6}$

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:

$x = 0.5$