Question

Explain in your own words how you would use your calculator to find the value of$co{t}^{-1}10$.

Short answer

The value of $co{t}^{-1}\left(10\right)$can be calculated by using the equivalent function${\tan }^{-1}\left(\frac{1}{10}\right)$.

Step-by-step solution

Step 1. Given information.

The function$co{t}^{-1}10$.

Step 2. Convert cotangent function to tangent.

Let,

$$\begin{gathered} co{t}^{-1}10=x \\ cotx=10 \\ so, \\ \tan x=\left(\frac{1}{cotx}\right) \\ =\left(\frac{1}{10}\right) \\ x={\tan }^{-1}\left(\frac{1}{10}\right) \end{gathered}$$

Step 3. Now, calculate the required value by using inverse tangent function in calculator. 

As,

$$\begin{gathered} co{t}^{-1}10=x \\ ={\tan }^{-1}\left(\frac{1}{10}\right) \end{gathered}$$

Now, use calculator and type ${\tan }^{-1}\left(\frac{1}{10}\right)$:

${\tan }^{-1}\left(\frac{1}{10}\right)\approx 5.71°$