Find the Reference Angle (9pi)/4

Problem

(9*π)/4

Solution

1. Identify the given angle θ=(9*π)/4 and determine if it is within the standard range of [0,2*π)

2. Find the coterminal angle by subtracting 2*π from the given angle until the result is between 0 and 2*π

(9*π)/4−2*π=(9*π)/4−(8*π)/4

(9*π)/4−(8*π)/4=π/4

3. Determine the quadrant of the coterminal angle π/4 Since 0<π/4<π/2 the angle lies in Quadrant I.

4. Apply the reference angle rule for Quadrant I, where the reference angle θ′ is equal to the angle itself.

θ′=π/4

Final Answer

Reference Angle of (9*π)/4=π/4

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