Trigonometry Examples

$y = \frac{3}{5} \cdot \sin (\frac{x}{7})$

Step 1

Rewrite the equation as $\frac{3}{5} \cdot \sin (\frac{x}{7}) = y$ .

$\frac{3}{5} \cdot \sin (\frac{x}{7}) = y$

Step 2

Multiply both sides of the equation by $\frac{5}{3}$ .

$\frac{5}{3} (\frac{3}{5} \sin (\frac{x}{7})) = \frac{5}{3} y$

Step 3

Simplify both sides of the equation.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Simplify $\frac{5}{3} (\frac{3}{5} \sin (\frac{x}{7}))$ .

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Step 3.1.1.1

Combine $\frac{3}{5}$ and $\sin (\frac{x}{7})$ .

$\frac{5}{3} \cdot \frac{3 \sin (\frac{x}{7})}{5} = \frac{5}{3} y$

Step 3.1.1.2

Cancel the common factor of $5$ .

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Step 3.1.1.2.1

Cancel the common factor.

$\frac{5}{3} \cdot \frac{3 \sin (\frac{x}{7})}{5} = \frac{5}{3} y$

Step 3.1.1.2.2

Rewrite the expression.

$\frac{1}{3} (3 \sin (\frac{x}{7})) = \frac{5}{3} y$

Step 3.1.1.3

Cancel the common factor of $3$ .

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Step 3.1.1.3.1

Factor $3$ out of $3 \sin (\frac{x}{7})$ .

$\frac{1}{3} (3 \sin (\frac{x}{7})) = \frac{5}{3} y$

Step 3.1.1.3.2

Cancel the common factor.

$\frac{1}{3} (3 \sin (\frac{x}{7})) = \frac{5}{3} y$

Step 3.1.1.3.3

Rewrite the expression.

$\sin (\frac{x}{7}) = \frac{5}{3} y$

Step 3.2

Simplify the right side.

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Step 3.2.1

Combine $\frac{5}{3}$ and $y$ .

$\sin (\frac{x}{7}) = \frac{5 y}{3}$

Step 4

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

$\frac{x}{7} = \arcsin (\frac{5 y}{3})$

Step 5

Multiply both sides of the equation by $7$ .

$7 \frac{x}{7} = 7 \arcsin (\frac{5 y}{3})$

Step 6

Simplify the left side.

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Step 6.1

Cancel the common factor of $7$ .

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Step 6.1.1

Cancel the common factor.

$7 \frac{x}{7} = 7 \arcsin (\frac{5 y}{3})$

Step 6.1.2

Rewrite the expression.

$x = 7 \arcsin (\frac{5 y}{3})$