Trigonometry Examples

$\cos (\frac{π}{4})$

Step 1

To convert radians to degrees, multiply by $\frac{180}{π}$ , since a full circle is $360 °$ or $2 π$ radians.

$(\cos (\frac{π}{4})) \cdot \frac{180 °}{π}$

Step 2

The exact value of $\cos (\frac{π}{4})$ is $\frac{\sqrt{2}}{2}$ .

$\frac{\sqrt{2}}{2} \cdot \frac{180}{π}$

Step 3

Cancel the common factor of $2$ .

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Step 3.1

Factor $2$ out of $180$ .

$\frac{\sqrt{2}}{2} \cdot \frac{2 (90)}{π}$

Step 3.2

Cancel the common factor.

$\frac{\sqrt{2}}{2} \cdot \frac{2 \cdot 90}{π}$

Step 3.3

Rewrite the expression.

$\sqrt{2} \cdot \frac{90}{π}$

Step 4

Combine $\sqrt{2}$ and $\frac{90}{π}$ .

$\frac{\sqrt{2} \cdot 90}{π}$

Step 5

Move $90$ to the left of $\sqrt{2}$ .

$\frac{90 \sqrt{2}}{π}$

Step 6

$π$ is approximately equal to $3.14159265$ .

$\frac{90 \sqrt{2}}{3.14159265}$

Step 7

Convert to a decimal.

$40.51423422 °$