Trigonometry Examples

$y = - 3 \csc (π x)$

Step 1

Rewrite the equation as $- 3 \csc (π x) = y$ .

$- 3 \csc (π x) = y$

Step 2

Divide each term in $- 3 \csc (π x) = y$ by $- 3$ and simplify.

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Step 2.1

Divide each term in $- 3 \csc (π x) = y$ by $- 3$ .

$\frac{- 3 \csc (π x)}{- 3} = \frac{y}{- 3}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $- 3$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{- 3 \csc (π x)}{- 3} = \frac{y}{- 3}$

Step 2.2.1.2

Divide $\csc (π x)$ by $1$ .

$\csc (π x) = \frac{y}{- 3}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Move the negative in front of the fraction.

$\csc (π x) = - \frac{y}{3}$

Step 3

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

$π x = arccsc (- \frac{y}{3})$

Step 4

Divide each term in $π x = arccsc (- \frac{y}{3})$ by $π$ and simplify.

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Step 4.1

Divide each term in $π x = arccsc (- \frac{y}{3})$ by $π$ .

$\frac{π x}{π} = \frac{arccsc (- \frac{y}{3})}{π}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $π$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{π x}{π} = \frac{arccsc (- \frac{y}{3})}{π}$

Step 4.2.1.2

Divide $x$ by $1$ .

$x = \frac{arccsc (- \frac{y}{3})}{π}$