Find the Reference Angle (11pi)/9

Problem

(11*π)/9

Solution

1. Identify the quadrant where the angle θ=(11*π)/9 resides by comparing it to the quadrantal angles 0 π/2 π and (3*π)/2

2. Determine that since π<(11*π)/9<(3*π)/2 (because (9*π)/9<(11*π)/9<(13.5*π)/9, the angle is in Quadrant III.

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

4. Subtract π from the given angle to find the reference angle.

θ′=(11*π)/9−π

5. Simplify the expression by finding a common denominator.

θ′=(11*π)/9−(9*π)/9

θ′=(2*π)/9

Final Answer

θ′=(2*π)/9

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