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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