Question

use a calculator to evaluate cot \\(\frac{\pi}{7}\\) .

a. 2.077

b. .422

c. 127.662

d. 24.17

Explanation:

Step1: Recall cotangent identity

Recall that \(\cot\theta=\frac{1}{\tan\theta}\), so we can find \(\tan\frac{\pi}{7}\) first and then take its reciprocal.

Step2: Set calculator to radian mode

Make sure the calculator is in radian mode (since the angle is given in radians, \(\frac{\pi}{7}\)).

Step3: Calculate \(\tan\frac{\pi}{7}\)

Using a calculator, \(\tan\frac{\pi}{7}\approx\tan(0.4488)\approx0.4816\) (approximate value of \(\frac{\pi}{7}\) is \(0.4488\) radians).

Step4: Find reciprocal for cotangent

Now, \(\cot\frac{\pi}{7}=\frac{1}{\tan\frac{\pi}{7}}\approx\frac{1}{0.4816}\approx2.077\).

Answer:

A. 2.077