Trigonometry Examples

$\frac{\cos (\frac{\sqrt{5}}{5})}{\sin (\frac{2 \sqrt{5}}{5})}$

Step 1

Rewrite $\frac{\cos (\frac{\sqrt{5}}{5})}{\sin (\frac{2 \sqrt{5}}{5})}$ as a product.

$\cos (\frac{\sqrt{5}}{5}) \frac{1}{\sin (\frac{2 \sqrt{5}}{5})}$

Step 2

Write $\cos (\frac{\sqrt{5}}{5})$ as a fraction with denominator $1$ .

$\frac{\cos (\frac{\sqrt{5}}{5})}{1} \cdot \frac{1}{\sin (\frac{2 \sqrt{5}}{5})}$

Step 3

Simplify.

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Step 3.1

Divide $\cos (\frac{\sqrt{5}}{5})$ by $1$ .

$\cos (\frac{\sqrt{5}}{5}) \frac{1}{\sin (\frac{2 \sqrt{5}}{5})}$

Step 3.2

Convert from $\frac{1}{\sin (\frac{2 \sqrt{5}}{5})}$ to $\csc (\frac{2 \sqrt{5}}{5})$ .

$\cos (\frac{\sqrt{5}}{5}) \csc (\frac{2 \sqrt{5}}{5})$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\cos (\frac{\sqrt{5}}{5}) \csc (\frac{2 \sqrt{5}}{5})$

Decimal Form:

$1.15619009 \dots$