Trigonometry Examples

$y = 2 \sin (3 x)$

Step 1

Rewrite the equation as $2 \sin (3 x) = y$ .

$2 \sin (3 x) = y$

Step 2

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

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Step 2.1

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

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

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $2$ .

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Step 2.2.1.1

Cancel the common factor.

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

Step 2.2.1.2

Divide $\sin (3 x)$ by $1$ .

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

Step 3

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

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

Step 4

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

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Step 4.1

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

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

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $3$ .

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Step 4.2.1.1

Cancel the common factor.

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

Step 4.2.1.2

Divide $x$ by $1$ .

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