Find the Reference Angle -315 degrees

Problem

−315^∘

Solution

1. Find a coterminal angle between 0^∘ and 360^∘ by adding 360^∘ to the given negative angle.

−315^∘+360^∘=45^∘

2. Identify the quadrant where the terminal side of the angle lies. Since 45^∘ is between 0^∘ and 90^∘ the angle is in Quadrant I.

0^∘<45^∘<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^′=45^∘

Final Answer

Reference Angle of −315^∘=45^∘

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