Find the Reference Angle (7pi)/10

Problem

(7*π)/10

Solution

1. Identify the quadrant in which the given angle θ=(7*π)/10 lies.

2. Compare the angle to the standard quadrantal angles. Since π/2<(7*π)/10<π (or 0.5*π<0.7*π<1.0*π, the angle is in Quadrant II.

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

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

θ′=π−(7*π)/10

5. Simplify the expression by finding a common denominator.

θ′=(10*π)/10−(7*π)/10

θ′=(3*π)/10

Final Answer

θ′=(3*π)/10

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