Question

How do you use a calculator to evaluate ${\tan ^{ - 1}}\left( {2.25} \right)$ in both radians and degrees?

Answer 1

Hint: Given the inverse trigonometric value. We have to find the exact value of inverse trigonometric angle in degrees and radians. First, we need to set the mode to degree or radian whichever required. Then, we will enter the value in the calculator and press enter button to compute the exact value of the expression.

Complete step-by-step solution:
We are given the inverse trigonometric value. First, set the Mode to degree to return the value of the expression in degrees.
First press the MODE button.
Then choose the DEGREE option.
Now, enter the trigonometric expression in the calculator by pressing the SHIFT and tan button on the calculator. Then, the screen of the calculator shows ${\tan ^{ - 1}}$. Then, enter the measure of an angle inside the brackets.
$ \Rightarrow {\tan ^{ - 1}}\left( {2.25} \right)$
Now, press Enter key to show the exact value of the expression.
$ \Rightarrow {\tan ^{ - 1}}\left( {2.25} \right) = 66.04^\circ $
Now, set the Mode to Radian to return the value of the expression in Radians.
First press the MODE button.
Then choose RADIANS option.
Now, again enter the trigonometric expression in the calculator by pressing the SHIFT and tan button on the calculator. Then, the screen of the calculator shows ${\tan ^{ - 1}}$. Then, enter the measure of an angle inside the brackets.
 $ \Rightarrow {\tan ^{ - 1}}\left( {2.25} \right)$
Now, press Enter key to show the exact value of the expression in radians.
$ \Rightarrow {\tan ^{ - 1}}\left( {2.25} \right) = 1.153$

Hence the value of ${\tan ^{ - 1}}\left( {2.25} \right)$ in radians is \[1.153\] and in degrees is $66.04^\circ $

Note: In such types of questions students mainly make mistakes while choosing the options which returns the result of the expression in desired format. Students mainly get confused while entering the ${\tan ^{ - 1}}$ in the calculator.