Trigonometry Examples

$y = 2 \sin (\frac{1}{3} x)$

Step 1

Rewrite the equation as $2 \sin (\frac{1}{3} x) = y$ .

$2 \sin (\frac{1}{3} x) = y$

Step 2

Divide each term in $2 \sin (\frac{1}{3} x) = y$ by $2$ and simplify.

Tap for more steps...

Step 2.1

Divide each term in $2 \sin (\frac{1}{3} x) = y$ by $2$ .

$\frac{2 \sin (\frac{1}{3} x)}{2} = \frac{y}{2}$

Step 2.2

Simplify the left side.

Tap for more steps...

Step 2.2.1

Cancel the common factor of $2$ .

Tap for more steps...

Step 2.2.1.1

Cancel the common factor.

$\frac{2 \sin (\frac{1}{3} x)}{2} = \frac{y}{2}$

Step 2.2.1.2

Divide $\sin (\frac{1}{3} x)$ by $1$ .

$\sin (\frac{1}{3} x) = \frac{y}{2}$

Step 3

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

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

Step 4

Simplify the left side.

Tap for more steps...

Step 4.1

Combine $\frac{1}{3}$ and $x$ .

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

Step 5

Multiply both sides of the equation by $3$ .

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

Step 6

Simplify the left side.

Tap for more steps...

Step 6.1

Cancel the common factor of $3$ .

Tap for more steps...

Step 6.1.1

Cancel the common factor.

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

Step 6.1.2

Rewrite the expression.

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