Find the Reference Angle 270

Problem

270^∘

Solution

1. Identify the position of the given angle on the coordinate plane. The angle 270^∘ lies exactly on the negative y-axis, which is the boundary between the third and fourth quadrants.

2. Recall the definition of a reference angle. The reference angle is the acute angle formed between the terminal side of the angle and the x-axis.

3. Calculate the distance from the terminal side to the nearest part of the x-axis. Since the terminal side is at 270^∘ the nearest points on the x-axis are 180^∘ and 360^∘

4. Subtract to find the difference: |270^∘−180^∘|=90^∘ or |270^∘−360^∘|=90^∘

Final Answer

(θ_ref)=90^∘

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