Precalculus Examples

$\frac{\cot (- t)}{\cos (- t)}$

Step 1

Rewrite $\cot (- t)$ in terms of sines and cosines.

$\frac{\frac{\cos (- t)}{\sin (- t)}}{\cos (- t)}$

Step 2

Rewrite $\frac{\frac{\cos (- t)}{\sin (- t)}}{\cos (- t)}$ as a product.

$\frac{\cos (- t)}{\sin (- t)} \cdot \frac{1}{\cos (- t)}$

Step 3

Cancel the common factor of $\cos (- t)$ .

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Step 3.1

Cancel the common factor.

$\frac{\cos (- t)}{\sin (- t)} \cdot \frac{1}{\cos (- t)}$

Step 3.2

Rewrite the expression.

$\frac{1}{\sin (- t)}$

Step 4

Since $\sin (- t)$ is an odd function, rewrite $\sin (- t)$ as $- \sin (t)$ .

$\frac{1}{- \sin (t)}$

Step 5

Cancel the common factor of $1$ and $- 1$ .

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Step 5.1

Rewrite $1$ as $- 1 (- 1)$ .

$\frac{- 1 (- 1)}{- \sin (t)}$

Step 5.2

Move the negative in front of the fraction.

$- \frac{1}{\sin (t)}$

Step 6

Convert from $\frac{1}{\sin (t)}$ to $\csc (t)$ .

$- \csc (t)$