Trigonometry Examples

$6 \arcsin (x) = 2 π$

Step 1

Divide each term in $6 \arcsin (x) = 2 π$ by $6$ and simplify.

Tap for more steps...

Step 1.1

Divide each term in $6 \arcsin (x) = 2 π$ by $6$ .

$\frac{6 \arcsin (x)}{6} = \frac{2 π}{6}$

Step 1.2

Simplify the left side.

Tap for more steps...

Step 1.2.1

Cancel the common factor of $6$ .

Tap for more steps...

Step 1.2.1.1

Cancel the common factor.

$\frac{6 \arcsin (x)}{6} = \frac{2 π}{6}$

Step 1.2.1.2

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

$\arcsin (x) = \frac{2 π}{6}$

Step 1.3

Simplify the right side.

Tap for more steps...

Step 1.3.1

Cancel the common factor of $2$ and $6$ .

Tap for more steps...

Step 1.3.1.1

Factor $2$ out of $2 π$ .

$\arcsin (x) = \frac{2 (π)}{6}$

Step 1.3.1.2

Cancel the common factors.

Tap for more steps...

Step 1.3.1.2.1

Factor $2$ out of $6$ .

$\arcsin (x) = \frac{2 π}{2 \cdot 3}$

Step 1.3.1.2.2

Cancel the common factor.

$\arcsin (x) = \frac{2 π}{2 \cdot 3}$

Step 1.3.1.2.3

Rewrite the expression.

$\arcsin (x) = \frac{π}{3}$

Step 2

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

$x = \sin (\frac{π}{3})$

Step 3

Simplify the right side.

Tap for more steps...

Step 3.1

The exact value of $\sin (\frac{π}{3})$ is $\frac{\sqrt{3}}{2}$ .

$x = \frac{\sqrt{3}}{2}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{\sqrt{3}}{2}$

Decimal Form:

$x = 0.86602540 \dots$