Find the Reference Angle 420

Problem

420^∘

Solution

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

420^∘−360^∘=60^∘

2. Identify the quadrant in which the coterminal angle lies. Since 60^∘ is between 0^∘ and 90^∘ it is in Quadrant I.

0^∘<60^∘<90^∘

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

θ^′=θ

4. Substitute the value to find the final result.

θ^′=60^∘

Final Answer

Reference Angle of *420^∘=60^∘

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