Find the Reference Angle -(5pi)/3

Problem

−(5*π)/3

Solution

1. Find a coterminal angle between 0 and 2*π by adding 2*π to the given negative angle.

θ=−(5*π)/3+2*π

2. Simplify the expression using a common denominator.

θ=−(5*π)/3+(6*π)/3

θ=π/3

3. Identify the quadrant of the coterminal angle. Since 0<π/3<π/2 the angle lies in Quadrant I.

Quadrant=I

4. Determine the reference angle θ^′ For an angle in Quadrant I, the reference angle is equal to the angle itself.

θ^′=θ

θ^′=π/3

Final Answer

Reference Angle of −(5*π)/3=π/3

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