Solve over the Interval cot(x)=-1.3 , (3pi)/2=x=2pi

Problem

cot(x)=−1.3,(3*π)/2≤x≤2*π

Solution

1. Convert to tangent by using the reciprocal identity tan(x)=1/cot(x)

tan(x)=1/(−1.3)

2. Calculate the reference angle by taking the inverse tangent of the absolute value of the ratio.

(x_ref)=arctan(1/1.3)

(x_ref)≈0.6558

3. Determine the quadrant based on the given interval (3*π)/2≤x≤2*π which corresponds to Quadrant IV.

4. Find the specific solution in Quadrant IV by subtracting the reference angle from 2*π

x=2*π−arctan(1/1.3)

x≈6.2832−0.6558

x≈5.6274

Final Answer

cot(x)=−1.3⇒x≈5.6274

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