Find the Reference Angle (11pi)/18

Problem

(11*π)/18

Solution

1. Identify the quadrant in which the angle θ=(11*π)/18 lies.

2. Compare the angle to the standard quadrantal boundaries in radians.

3. Observe that π/2<(11*π)/18<π because (9*π)/18<(11*π)/18<(18*π)/18

4. Determine that the angle is in Quadrant II.

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

6. Subtract the given angle from π

θ′=π−(11*π)/18

7. Simplify the expression by finding a common denominator.

θ′=(18*π)/18−(11*π)/18

θ′=(7*π)/18

Final Answer

θ′=(7*π)/18

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