Trigonometry Examples

\csc (θ) = \frac{1}{\sin (θ)}

$\csc (θ) = \frac{1}{\sin (θ)}$

Step 1

Subtract

\frac{1}{\sin (θ)}

$\frac{1}{\sin (θ)}$ from both sides of the equation.

\csc (θ) - \frac{1}{\sin (θ)} = 0

$\csc (θ) - \frac{1}{\sin (θ)} = 0$

Step 2

Simplify

\csc (θ) - \frac{1}{\sin (θ)}

$\csc (θ) - \frac{1}{\sin (θ)}$ .

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Step 2.1

Rewrite

\csc (θ)

$\csc (θ)$ in terms of sines and cosines.

\frac{1}{\sin (θ)} - \frac{1}{\sin (θ)} = 0

$\frac{1}{\sin (θ)} - \frac{1}{\sin (θ)} = 0$

Step 2.2

Subtract

\frac{1}{\sin (θ)}

$\frac{1}{\sin (θ)}$ from

\frac{1}{\sin (θ)}

$\frac{1}{\sin (θ)}$ .

0 = 0

$0 = 0$

0 = 0

$0 = 0$

Step 3

The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.