Trigonometry Examples

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

Step 1

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

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

Step 2

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

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

Step 3

Simplify the left side.

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Step 3.1

Combine $\frac{1}{2}$ and $x$ .

$\frac{x}{2} = arccsc (y)$

Step 4

Multiply both sides of the equation by $2$ .

$2 \frac{x}{2} = 2 arccsc (y)$

Step 5

Simplify the left side.

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Step 5.1

Cancel the common factor of $2$ .

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Step 5.1.1

Cancel the common factor.

$2 \frac{x}{2} = 2 arccsc (y)$

Step 5.1.2

Rewrite the expression.

$x = 2 arccsc (y)$