Find the Reference Angle (3pi)/2

Problem

(3*π)/2

Solution

1. Identify the position of the given angle θ=(3*π)/2 on the unit circle.

2. Determine the quadrant or axis where the angle terminates. The angle (3*π)/2 (or 270 lies exactly on the negative y-axis, which is a quadrantal angle.

3. Apply the definition of a reference angle, which is the acute angle θ′ formed between the terminal side of the angle and the x-axis.

4. Calculate the distance to the nearest part of the x-axis. The terminal side at (3*π)/2 is equidistant from the positive x-axis (2*π and the negative x-axis (π.

5. Subtract the nearest x-axis value from the angle or vice versa to find the positive acute difference: (3*π)/2−π=π/2 or 2*π−(3*π)/2=π/2

Final Answer

Reference Angle of (3*π)/2=π/2

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