Find the Reference Angle (17pi)/3

Problem

(17*π)/3

Solution

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

2*π=(6*π)/3

(17*π)/3−2⋅(6*π)/3=(17*π)/3−(12*π)/3

(17*π)/3≡(5*π)/3

2. Identify the quadrant for the angle (5*π)/3 Since (3*π)/2<(5*π)/3<2*π the angle lies in Quadrant IV.

3. Apply the reference angle formula for Quadrant IV, which is θ′=2*π−θ

θ′=2*π−(5*π)/3

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

θ′=(6*π)/3−(5*π)/3

θ′=π/3

Final Answer

Reference Angle of (17*π)/3=π/3

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