Problem 54 - Precalculus: A Concise Course

Question

Use a calculator to evaluate each function. Round your answers to four decimal places. (Be sure the calculator is in the correct angle mode.) (a) \(\cot 11^{\circ} 15^{\prime}\) (b) \(\tan 11^{\circ} 15^{\prime}\)

Step-by-Step Solution

Answer

The cotangent of 11 degrees 15 minutes is approximately 4.7043, and the tangent of 11 degrees 15 minutes is approximately 0.2126.

Step 1: Convert Degrees and Minutes to Decimal Degree Form

First, convert the degrees and minutes into decimal degree form. Recall that there are 60 minutes in a degree. Therefore, the conversion would be \(11^{\circ} 15^{\prime}\) to \(11.25^{\circ}\). This is done by dividing the number of minutes by 60 and then adding it to the number of degrees.

Step 2: Evaluate the Cotangent Function

Use your calculator to find the cotangent of 11.25 degrees. Make sure your calculator is in degree mode. The cotangent can be found by taking the reciprocal of the tangent function, \(\cot(\theta) = 1/\tan(\theta)\). Calculate \(\cot 11.25^{\circ}=1/\tan 11.25^{\circ}\) and round your answer to four decimal places.

Step 3: Evaluate the Tangent Function

Next, use your calculator to find the tangent of 11.25 degrees. Make sure your calculator is still in degree mode. Calculate \(\tan 11.25^{\circ}\) and round your answer to four decimal places.