Find the Reference Angle (7pi)/12

Problem

(7*π)/12

Solution

1. Determine the quadrant of the given angle θ=(7*π)/12 Since π/2<(7*π)/12<π (which is (6*π)/12<(7*π)/12<(12*π)/12, the angle lies in Quadrant II.

2. Apply the reference angle formula for Quadrant II. The reference angle θ′ is found by subtracting the angle from π

θ′=π−θ

3. Substitute the value of θ into the formula.

θ′=π−(7*π)/12

4. Find a common denominator to perform the subtraction.

θ′=(12*π)/12−(7*π)/12

5. Subtract the numerators to find the final reference angle.

θ′=(5*π)/12

Final Answer

θ′=(5*π)/12

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