Find the Reference Angle 285

Problem

285^∘

Solution

1. Identify the quadrant in which the given angle θ=285^∘ lies. Since 270^∘<285^∘<360^∘ the angle is in the fourth quadrant.

2. Apply the formula for the reference angle θ^′ in the fourth quadrant. The reference angle is the positive acute angle formed by the terminal side of θ and the x-axis.

3. Calculate the difference between 360^∘ and the given angle.

θ^′=360^∘−285^∘

4. Subtract the values to find the final result.

θ^′=75^∘

Final Answer

θ^′=75^∘

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