Trigonometry Examples

$\frac{\sec (t)}{\tan (t)}$

Step 1

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

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

Step 2

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

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

Step 3

Multiply by the reciprocal of the fraction to divide by $\frac{\sin (t)}{\cos (t)}$ .

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

Step 4

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

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Step 4.1

Cancel the common factor.

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

Step 4.2

Rewrite the expression.

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

Step 5

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

$\csc (t)$