Find the Reference Angle 315 degrees

Problem

315^∘

Solution

1. Identify the quadrant in which the given angle θ=315^∘ lies. Since 270^∘<315^∘<360^∘ the angle is in Quadrant IV.

2. Apply the formula for the reference angle θ^′ in Quadrant IV, which is θ^′=360^∘−θ

3. Substitute the value of the angle into the formula: θ^′=360^∘−315^∘

4. Subtract the values to find the reference angle.

Final Answer

θ^′=45^∘

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