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

Problem

cot(−(3*π)/4)

Solution

1. Apply the odd-even property of the cotangent function, which states that cot(−x)=−cot(x)

cot(−(3*π)/4)=−cot((3*π)/4)

2. Identify the reference angle for (3*π)/4 Since the angle is in the second quadrant, the reference angle is π−(3*π)/4=π/4

Reference Angle=π/4

3. Determine the sign of the cotangent function in the second quadrant. In Quadrant II, cos(x) is negative and sin(x) is positive, so cot(x)=cos(x)/sin(x) is negative.

cot((3*π)/4)=−cot(π/4)

4. Substitute the known value for cot(π/4) which is 1

cot((3*π)/4)=−1

5. Combine the results by substituting the value back into the expression from step 1.

−(−1)=1

Final Answer

cot(−(3*π)/4)=1

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