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Chapter 4: Problem 89

Use a calculator to evaluate the trigonometric function. Round your answer to four decimal places. (Be sure the calculator is in the correct mode.) $$\cot \left(-\frac{11 \pi}{8}\right)$$

Short Answer

Expert verified
Assuming the tangent value given by the calculator is correct and rounded already to four decimal places, the short answer would be the reciprocal of this value also rounded to four decimal places. The exact value cannot be determined without the calculator result from Step 3.

Step by step solution

01

Convert Cotangent to Reciprocal of Tangent

The first step is to recognize that the cotangent of an angle is the reciprocal of the tangent of the same angle. Therefore, the problem is equivalent to computing the reciprocal of \(\tan(-\frac{11 \pi}{8})\).
02

Ensure Calculator is in Radian Mode

Before utilizing a calculator, check that it is in radian mode. This step is crucial because \(-\frac{11 \pi}{8}\) is given in radians, not degrees.
03

Calculate Tangent

Use the calculator to find the value of \(\tan(-\frac{11 \pi}{8})\).
04

Compute Reciprocal

Take the reciprocal of the value computed in Step 3. This step gives the value of \(\cot(-\frac{11 \pi}{8})\).
05

Round to Four Decimal Places

As the final step, round the result from Step 4 to four decimal places. This result gives the final answer.

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