Question

How do you evaluate \[{\tan ^{ - 1}}\left( {\dfrac{4}{3}} \right)\] on Scientific Calculator?

Answer 1

Hint: In order to use inverse trigonometric functions, we need to understand that an inverse trigonometric function the domain of the inverse function is the range of the original function, and vice versa. To find the calculator is set to Degree mode. To convert a trigonometric ratio back to an angle measure, use the inverse function found above the same key as the function. Press, select the inverse function, either \[{\sin ^{ - 1}}\] , \[{\cos ^{ - 1}}\] , or \[{\tan ^{ - 1}}\] and enter the ratio. Then, close the parenthesis and select the option.

Complete step-by-step answer:
The given function is
 \[{\tan ^{ - 1}}\left( {\dfrac{4}{3}} \right)\] .
To find the inverse, it will depend upon your calculator. Look for one of the following: \[{\tan ^{ - 1}}\] , \[\operatorname{Arctan} \] or atan.
Typically, this would be a "2nd function" key,
So, use
"2nd Function",
 \[{\tan ^{ - 1}}\] (or whatever is the given function), as given here: \[{\tan ^{ - 1}}\left( {\dfrac{4}{3}} \right)\] or \[{\tan ^{ - 1}}\left( {1.33} \right)\]
Then press " ENTER " or "=" key.
The inverse value is displayed as 53. 0612..
On TI-84 calculator,
Enter the inverse trigonometric function of the trigonometric value i.e., given \[{\tan ^{ - 1}}\left( {\dfrac{4}{3}} \right)\] to convert to degrees. First press the 2nd key, then press the key for the trigonometric function at hand. For example, we want to convert the tan inverse of 1.33 into degrees, press 2nd and then press Tan. The display will show \[{\tan ^{ - 1}}\] , or inverse tan. Now enter 1.33 and a closing parenthesis.
Press ENTER and collect your answer. The result should be a number, expressed in degrees. For example, if you entered \[{\tan ^{ - 1}}\] of 1.33 and hit enter, the calculator will display 53.0612, which is 53 degrees. Be sure to remember the closing parenthesis.
Hence, in this way we can find the value of inverse trig functions using calculators.

Note: We must note that \[{\tan ^{ - 1}}\] returns a value in degrees and the other four return values in radians. You can easily convert the basic trigonometric functions into angles measured in degrees or radians using a TI-84 Plus calculator. The TI-84 Plus is capable of going in both directions - from the angle to the trigonometric measure.