Find the Reference Angle (5pi)/2

Problem

(5*π)/2

Solution

1. Identify the given angle θ=(5*π)/2

2. Find the coterminal angle within the standard range [0,2*π) by subtracting multiples of 2*π

3. Subtract 2*π from the given angle:

(5*π)/2−2*π=(5*π)/2−(4*π)/2

4. Simplify the result to find the coterminal angle:

(5*π)/2−(4*π)/2=π/2

5. Determine the reference angle. Since π/2 lies on the positive y-axis (a quadrantal angle), the reference angle is the acute angle formed with the x-axis.

6. Calculate the distance to the nearest x-axis:

|π/2−0|=π/2

Final Answer

Reference Angle of (5*π)/2=π/2

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