Evaluate (11pi)/3

Problem

(11*π)/3

Solution

1. Identify the angle in terms of its position on the unit circle by finding a coterminal angle within the standard range [0,2*π)

2. Divide the numerator by the denominator to express the fraction as a mixed number.

(11*π)/3=32/3*π

3. Subtract multiples of 2*π to find the coterminal angle.

(11*π)/3−2*π=(11*π)/3−(6*π)/3

(11*π)/3−2*π=(5*π)/3

4. Determine the quadrant and reference angle. The angle (5*π)/3 is in Quadrant IV, and its reference angle is 2*π−(5*π)/3=π/3

5. Evaluate the position. In Quadrant IV, the coordinates on the unit circle are (cos(π/3),−sin(π/3))

cos((5*π)/3)=1/2

sin((5*π)/3)=−√(,3)/2

Final Answer

(11*π)/3=(5*π)/3

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