Q. 71 - Precalculus Enhanced with Graphing Utilities

Question

Use a calculator to find the approximate value of each expression rounded to two decimal places: $\cot \left(\frac{\mathrm{\pi }}{12}\right)$

Step-by-Step Solution

Answer

The approximate value of $\cot \left(\frac{\mathrm{\pi }}{12}\right)$ is $3.73$

Step 1. Given information

We are given an expression $\cot \left(\frac{\mathrm{\pi }}{12}\right)$.

We have to use the calculator to find the approximate value of the above expression and round it off to two decimal places.

Step 2. Concept

• Note that $\cot \theta =\frac{1}{\tan \theta }$
• While using the calculator to find the values of trigonometric expression, set the calculator to the correct MODE depending on whether you are entering the angle using degree or radian.

Step 3. Finding the approximate value of the given expression

The given trigonometric expression is, $\cot \left(\frac{\mathrm{\pi }}{12}\right)$

Since the angle is in radians, set the MODE in the calculator to receive radians. 

As we know, most of the calculators do not have the cot key. Therefore, We will make use of the relation that $\cot \theta = \frac{1}{\tan \theta }$

Therefore, entering the given data in the calculator we have, 

$$\begin{gathered} \cot \left(\frac{\mathrm{\pi }}{12}\right)=\frac{1}{\tan \left(\frac{\mathrm{\pi }}{12}\right)} \\ \Rightarrow \cot \left(\frac{\mathrm{\pi }}{12}\right)\approx 3.73 \end{gathered}$$

which is rounded to two decimal places.

Step 4. Final Answer

The approximate value of the expression $\cot \left(\frac{\mathrm{\pi }}{12}\right)$ after rounding off to two decimal places is $3.73$ .