Find the Reference Angle -(7pi)/9

Problem

−(7*π)/9

Solution

1. Find a coterminal angle in the interval [0,2*π] by adding 2*π to the given angle.

θ=−(7*π)/9+2*π

θ=−(7*π)/9+(18*π)/9

θ=(11*π)/9

2. Determine the quadrant where the angle (11*π)/9 terminates. Since π<(11*π)/9<(3*π)/2 (or 180<220<270, the angle is in Quadrant III.

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

θ′=(11*π)/9−π

θ′=(11*π)/9−(9*π)/9

θ′=(2*π)/9

Final Answer

θ′=(2*π)/9

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