Precalculus Examples

$- 465 °$

Step 1

Find an angle that is positive, less than $360 °$ , and coterminal with $- 465 °$ .

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Step 1.1

Add $360 °$ to $- 465 °$ .

$- 465 ° + 360 °$

Step 1.2

The resulting angle of $- 105 °$ is coterminal with $- 465 °$ but isn't positive. Repeat the step.

$- 105 °$

Step 1.3

Add $360 °$ to $- 105 °$ .

$- 105 ° + 360 °$

Step 1.4

The resulting angle of $255 °$ is positive and coterminal with $- 465 °$ .

$255 °$

Step 2

Since the angle $180 °$ is in the third quadrant, subtract $180 °$ from $255 °$ .

$255 ° - 180 °$

Step 3

Subtract $180$ from $255$ .

$75 °$