Find the Reference Angle (15pi)/4

Problem

(15*π)/4

Solution

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

(15*π)/4−2*π=(15*π)/4−(8*π)/4

(15*π)/4−(8*π)/4=(7*π)/4

2. Identify the quadrant for the angle (7*π)/4 Since (3*π)/2<(7*π)/4<2*π the angle lies in Quadrant IV.

3. Apply the reference angle formula for Quadrant IV, which is θ′=2*π−θ

θ′=2*π−(7*π)/4

4. Simplify the expression to find the final reference angle.

θ′=(8*π)/4−(7*π)/4

θ′=π/4

Final Answer

Reference Angle of (15*π)/4=π/4

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