Find the Reference Angle -420 degrees

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Trigonometry

$- 420 °$

Find an angle that is positive, less than $360 °$ , and coterminal with $- 420 °$ .

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Add $360 °$ to $- 420 °$ .

$- 420 ° + 360 °$

The resulting angle of $- 60 °$ is coterminal with $- 420 °$ but isn't positive. Repeat the step.

$- 60 °$

Add $360 °$ to $- 60 °$ .

$- 60 ° + 360 °$

The resulting angle of $300 °$ is positive and coterminal with $- 420 °$ .

$300 °$

Since the angle $300 °$ is in the fourth quadrant, subtract $300 °$ from $360 °$ .

$360 ° - 300 °$

Subtract $300$ from $360$ .

$60 °$

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