Find the Exact Value cot((3pi)/4)

Problem

cot((3*π)/4)

Solution

1. Identify the angle (3*π)/4 on the unit circle. This angle is in the second quadrant.

2. Determine the reference angle by subtracting the angle from π

Reference Angle=π−(3*π)/4

Reference Angle=π/4

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

cot((3*π)/4)=cos((3*π)/4)/sin((3*π)/4)

4. Evaluate the sine and cosine values for (3*π)/4 In the second quadrant, cosine is negative and sine is positive.

cos((3*π)/4)=−√(,2)/2

sin((3*π)/4)=√(,2)/2

5. Substitute these values into the cotangent expression and simplify.

cot((3*π)/4)=(−√(,2)/2)/√(,2)/2

cot((3*π)/4)=−1

Final Answer

cot((3*π)/4)=−1

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