Find the Reference Angle (24pi)/7

Problem

(24*π)/7

Solution

1. Identify the given angle θ=(24*π)/7 and determine its position relative to a full rotation of 2*π radians.

2. Find the coterminal angle by subtracting multiples of 2*π until the angle is within the interval [0,2*π)

(24*π)/7−2*π=(24*π)/7−(14*π)/7

(24*π)/7−(14*π)/7=(10*π)/7

3. Determine the quadrant for the coterminal angle (10*π)/7 Since π<(10*π)/7<(3*π)/2 the angle lies in Quadrant III.

4. Apply the reference angle formula for Quadrant III, which is θ′=θ−π

θ′=(10*π)/7−π

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

θ′=(10*π)/7−(7*π)/7

θ′=(3*π)/7

Final Answer

Reference Angle of (24*π)/7=(3*π)/7

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