Find the Reference Angle (25pi)/6

Problem

(25*π)/6

Solution

1. Identify the given angle θ=(25*π)/6

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

3. Calculate the number of full rotations:

(25*π)/6=4*π+π/6

4. Subtract 4*π (which is 2×2*π to find the coterminal angle θ′

θ′=(25*π)/6−(24*π)/6

θ′=π/6

5. Determine the quadrant of the coterminal angle. Since 0<π/6<π/2 the angle is in Quadrant I.

6. Apply the reference angle rule for Quadrant I, where the reference angle (θ_R) is equal to the angle itself.

(θ_R)=π/6

Final Answer

Reference Angle of (25*π)/6=π/6

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