Trigonometry Examples

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

Step 1

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

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

Step 2

Multiply both sides of the equation by $2$ .

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

Step 3

Simplify the left side.

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Step 3.1

Simplify $2 (\frac{1}{2} \sin (3 x))$ .

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Step 3.1.1

Combine $\frac{1}{2}$ and $\sin (3 x)$ .

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

Step 3.1.2

Cancel the common factor of $2$ .

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Step 3.1.2.1

Cancel the common factor.

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

Step 3.1.2.2

Rewrite the expression.

$\sin (3 x) = 2 y$

Step 4

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

$3 x = \arcsin (2 y)$

Step 5

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

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Step 5.1

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

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

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $3$ .

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Step 5.2.1.1

Cancel the common factor.

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

Step 5.2.1.2

Divide $x$ by $1$ .

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