Trigonometry Examples

$y = \sin (520 π x)$

Step 1

Rewrite the equation as $\sin (520 π x) = y$ .

$\sin (520 π x) = y$

Step 2

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

$520 π x = \arcsin (y)$

Step 3

Divide each term in $520 π x = \arcsin (y)$ by $520 π$ and simplify.

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Step 3.1

Divide each term in $520 π x = \arcsin (y)$ by $520 π$ .

$\frac{520 π x}{520 π} = \frac{\arcsin (y)}{520 π}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $520$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{520 π x}{520 π} = \frac{\arcsin (y)}{520 π}$

Step 3.2.1.2

Rewrite the expression.

$\frac{π x}{π} = \frac{\arcsin (y)}{520 π}$

Step 3.2.2

Cancel the common factor of $π$ .

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Step 3.2.2.1

Cancel the common factor.

$\frac{π x}{π} = \frac{\arcsin (y)}{520 π}$

Step 3.2.2.2

Divide $x$ by $1$ .

$x = \frac{\arcsin (y)}{520 π}$