Trigonometry Examples

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

Step 1

Set the argument in $\csc (\frac{x}{2})$ equal to $π n$ to find where the expression is undefined.

$\frac{x}{2} = π n$ , for any integer $n$

Step 2

Solve for $x$ .

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Step 2.1

Multiply both sides of the equation by $2$ .

$2 \frac{x}{2} = 2 (π n)$

Step 2.2

Simplify both sides of the equation.

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Step 2.2.1

Simplify the left side.

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Step 2.2.1.1

Cancel the common factor of $2$ .

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Step 2.2.1.1.1

Cancel the common factor.

$2 \frac{x}{2} = 2 (π n)$

Step 2.2.1.1.2

Rewrite the expression.

$x = 2 (π n)$

Step 2.2.2

Simplify the right side.

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Step 2.2.2.1

Remove parentheses.

$x = 2 π n$

Step 3

The equation is undefined where the denominator equals $0$ , the argument of a square root is less than $0$ , or the argument of a logarithm is less than or equal to $0$ .

${x | x = 2 π n}$ $n$ , for any integer $n$

Step 4