Trigonometry Examples

$\frac{\sec (θ)}{\tan (θ)}$

Step 1

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

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

Step 2

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

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

Step 3

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

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

Step 4

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

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Step 4.1

Cancel the common factor.

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

Step 4.2

Rewrite the expression.

$\frac{1}{\sin (θ)}$

Step 5

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

$\csc (θ)$