Find the Reference Angle -(8pi)/3

Problem

−(8*π)/3

Solution

1. Find a coterminal angle within the range [0,2*π] by adding multiples of 2*π

θ=−(8*π)/3+2*π=−(8*π)/3+(6*π)/3=−(2*π)/3

θ=−(2*π)/3+2*π=−(2*π)/3+(6*π)/3=(4*π)/3

2. Identify the quadrant where the angle (4*π)/3 terminates.

π<(4*π)/3<(3*π)/2

The angle is in Quadrant III.

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

θ′=(4*π)/3−π

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

θ′=(4*π)/3−(3*π)/3=π/3

Final Answer

Reference Angle of −(8*π)/3=π/3

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