Trigonometry Examples

$\sec (- \frac{π}{18}) \cos (\frac{37 π}{18})$

Step 1

Add full rotations of $2 π$ until the angle is greater than or equal to $0$ and less than $2 π$ .

$\sec (\frac{35 π}{18}) \cos (\frac{37 π}{18})$

Step 2

Rewrite $\sec (\frac{35 π}{18})$ in terms of sines and cosines.

$\frac{1}{\cos (\frac{35 π}{18})} \cos (\frac{37 π}{18})$

Step 3

Subtract full rotations of $2 π$ until the angle is greater than or equal to $0$ and less than $2 π$ .

$\frac{1}{\cos (\frac{35 π}{18})} \cos (\frac{π}{18})$

Step 4

Combine $\frac{1}{\cos (\frac{35 π}{18})}$ and $\cos (\frac{π}{18})$ .

$\frac{\cos (\frac{π}{18})}{\cos (\frac{35 π}{18})}$

Step 5

Rewrite $\frac{\cos (\frac{π}{18})}{\cos (\frac{35 π}{18})}$ as a product.

$\cos (\frac{π}{18}) \frac{1}{\cos (\frac{35 π}{18})}$

Step 6

Write $\cos (\frac{π}{18})$ as a fraction with denominator $1$ .

$\frac{\cos (\frac{π}{18})}{1} \cdot \frac{1}{\cos (\frac{35 π}{18})}$

Step 7

Simplify.

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Step 7.1

Divide $\cos (\frac{π}{18})$ by $1$ .

$\cos (\frac{π}{18}) \frac{1}{\cos (\frac{35 π}{18})}$

Step 7.2

Convert from $\frac{1}{\cos (\frac{35 π}{18})}$ to $\sec (\frac{35 π}{18})$ .

$\cos (\frac{π}{18}) \sec (\frac{35 π}{18})$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\cos (\frac{π}{18}) \sec (\frac{35 π}{18})$

Decimal Form:

$1$