Find the Reference Angle 420 degrees

Problem

420^∘

Solution

1. Find the coterminal angle between 0^∘ and 360^∘ by subtracting 360^∘ from the given angle.

420^∘−360^∘=60^∘

2. Identify the quadrant where the coterminal angle 60^∘ lies. Since 0^∘<60^∘<90^∘ the angle is in Quadrant I.

3. Determine the reference angle based on the quadrant rules. For an angle θ in Quadrant I, the reference angle θ^′ is equal to the angle itself.

θ^′=60^∘

Final Answer

Reference Angle of *420^∘=60^∘

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