Precalculus Examples

$- \frac{\sec (20)}{\csc (70)}$

Step 1

Rewrite $\csc (70)$ in terms of sines and cosines.

$- \frac{\sec (20)}{\frac{1}{\sin (70)}}$

Step 2

Rewrite $\sec (20)$ in terms of sines and cosines.

$- \frac{\frac{1}{\cos (20)}}{\frac{1}{\sin (70)}}$

Step 3

Multiply by the reciprocal of the fraction to divide by $\frac{1}{\sin (70)}$ .

$- (\frac{1}{\cos (20)} \sin (70))$

Step 4

Write $\sin (70)$ as a fraction with denominator $1$ .

$- (\frac{1}{\cos (20)} \cdot \frac{\sin (70)}{1})$

Step 5

Simplify.

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Step 5.1

Divide $\sin (70)$ by $1$ .

$- (\frac{1}{\cos (20)} \sin (70))$

Step 5.2

Convert from $\frac{1}{\cos (20)}$ to $\sec (20)$ .

$- (\sec (20) \sin (70))$

$- \sec (20) \sin (70)$

Step 6

The result can be shown in multiple forms.

Exact Form:

$- \sec (20) \sin (70)$

Decimal Form:

$- 1.000000000000 \dots$