Find the Exact Value cos((11pi)/2)

Problem

cos((11*π)/2)

Solution

1. Simplify the angle by finding its coterminal equivalent within the interval [0,2*π)

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

(11*π)/2=5.5*π

3. Subtract multiples of 2*π until the angle is within the standard range.

5.5*π−2*π=3.5*π

3.5*π−2*π=1.5*π

4. Convert the decimal back to a fraction to identify the position on the unit circle.

1.5*π=(3*π)/2

5. Identify the coordinates on the unit circle at the angle (3*π)/2

Point=(0,−1)

6. Evaluate the cosine function, which corresponds to the xcoordinate of the point.

cos((3*π)/2)=0

Final Answer

cos((11*π)/2)=0

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