Find the Exact Value sin((27pi)/2)

Problem

sin((27*π)/2)

Solution

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

2. Divide the coefficient 27 by the denominator 2 to express the fraction as a mixed number.

(27*π)/2=13.5*π

3. Subtract the largest multiple of 2*π that is less than or equal to the angle to find the coterminal angle.

13.5*π−12*π=1.5*π

4. Convert the result back to a fraction.

1.5*π=(3*π)/2

5. Evaluate the sine function at the coterminal angle (3*π)/2 using the unit circle.

sin((3*π)/2)=−1

Final Answer

sin((27*π)/2)=−1

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