Trigonometry Examples

$\cos (495)$

Step 1

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

Step 2

Remove full rotations of $360$ ° until the angle is between $0$ ° and $360$ °.

$\cos (135) \cdot \frac{π}{180}$ radians

Step 3

Apply the reference angle by finding the angle with equivalent trig values in the first quadrant. Make the expression negative because cosine is negative in the second quadrant.

$- \cos (45) \cdot \frac{π}{180}$ radians

Step 4

The exact value of $\cos (45)$ is $\frac{\sqrt{2}}{2}$ .

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

Step 5

Multiply $- \frac{\sqrt{2}}{2} \cdot \frac{π}{180}$ .

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Step 5.1

Multiply $\frac{π}{180}$ by $\frac{\sqrt{2}}{2}$ .

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

Step 5.2

Multiply $180$ by $2$ .

$- \frac{π \sqrt{2}}{360}$ radians