Question

use a calculator to find the value of the trigonometric function.

\\( \cot \frac { 5 \pi } { 12 } \\)

\\( \cot \frac { 5 \pi } { 12 } \approx \square \\) (round to four decimal places as needed.)

Explanation:

Step1: Use the reciprocal identity

Since \(\cot\theta=\frac{1}{\tan\theta}\), then \(\cot\frac{5\pi}{12}=\frac{1}{\tan\frac{5\pi}{12}}\).

Step2: Calculate \(\tan\frac{5\pi}{12}\)

Using a calculator in radian mode, \(\tan\frac{5\pi}{12}\approx3.73205080757\).

Step3: Calculate \(\cot\frac{5\pi}{12}\)

\(\cot\frac{5\pi}{12}=\frac{1}{\tan\frac{5\pi}{12}}\approx\frac{1}{3.73205080757}\approx0.2679\)

Answer:

\(0.2679\)