Find the Exact Value cot((15pi)/2)

Problem

cot((15*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.

(15*π)/2=7.5*π

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

7.5*π−6*π=1.5*π

4. Convert back to fraction form.

1.5*π=(3*π)/2

5. Apply the definition of the cotangent function in terms of sine and cosine.

cot((3*π)/2)=cos((3*π)/2)/sin((3*π)/2)

6. Evaluate the trigonometric values at the quadrantal angle (3*π)/2

cos((3*π)/2)=0

sin((3*π)/2)=−1

7. Calculate the final ratio by substituting the values.

0/(−1)=0

Final Answer

cot((15*π)/2)=0

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