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

Problem

cos((27*π)/2)

Solution

1. Simplify the angle by dividing the numerator by the denominator to find the number of full rotations.

(27*π)/2=13.5*π

2. Subtract multiples of 2*π to find the coterminal angle within the interval [0,2*π)

13.5*π−12*π=1.5*π

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

1.5*π=(3*π)/2

4. Identify the coordinates on the unit circle at (3*π)/2 radians, which is the negative y-axis.

(x,y)=(0,−1)

5. Determine the cosine value, which corresponds to the x-coordinate of the point.

cos((3*π)/2)=0

Final Answer

cos((27*π)/2)=0

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