Question

How do you use a calculator to evaluate $\cot \left( {1.5\pi } \right)$?

Answer 1

Hint: In this question we have to find the value of the given trigonometric angle using a calculator.
This is done by pressing followed by the Tan key and the value then press 1 followed by “$ \div $” then we will get the required answer by pressing “ENTER”.

Complete step by step solution:
Given trigonometric angle is $\cot \left( {1.5\pi } \right)$,
As we know that from the trigonometric identities, $\cot x = \dfrac{1}{{\tan x}}$,
So, as cot function will not be there in the calculator as a default function will have to find the tan value for the given angle.
Now to find the value we will use graphing calculator like T1-84,
To evaluate the trigonometric functions in the calculator we first press “TAN” key to enter, now we enter parenthesis and enter the given angle i.e., $1.5\pi $, which can be written in degrees as$ \div $ $1.5\pi = 1.5\left( {{{180}^o}} \right) = {270^o}$,
So, having entered all the values , we now press the “ENTER” key, after pressing the “ENTER” key the calculator immediately shows the answer as “UNDEFINED” which is in degrees as the default mode of the calculator for angle measurements in degrees. We can also change the degrees to radians just by pressing the “MODE” key.
Now press 1 followed by “$ \div $” division operation then we the calculator immediately shows result as 0 as $\dfrac{1}{\infty } = 0$,
So, the value of $\cot \left( {1.5\pi } \right)$ is 0.

Final Answer:
$\therefore $The value of the given trigonometric angle $\cot \left( {1.5\pi } \right)$will be equal to $0$.

Note:
The inverse trig functions are generally the second [2nd] functions of the trigonometry buttons in the calculator. We should also get in the habit of using the $\pi $ button instead of typing in 3.14159 ... for $\pi $. Most calculators don't have [sec], [csc] and [cot] functions because it's easy enough to type in$\dfrac{1}{{\sin x}}$, $\dfrac{1}{{\cos x}}$, or $\dfrac{1}{{\tan x}}$ . Make sure you always know which angle units your calculator is set to use: radians or degrees. Know how to switch between them.