Find the Reference Angle -580 degrees

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Trigonometry

$- 580 °$

Find an angle that is positive, less than $360 °$ , and coterminal with $- 580 °$ .

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Add $360 °$ to $- 580 °$ .

$- 580 ° + 360 °$

The resulting angle of $- 220 °$ is coterminal with $- 580 °$ but isn't positive. Repeat the step.

$- 220 °$

Add $360 °$ to $- 220 °$ .

$- 220 ° + 360 °$

The resulting angle of $140 °$ is positive and coterminal with $- 580 °$ .

$140 °$

Since the angle $140 °$ is in the second quadrant, subtract $140 °$ from $180 °$ .

$180 ° - 140 °$

Subtract $140$ from $180$ .

$40 °$

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