Question

How do you use a calculator to approximate ${\tan ^{ - 1}}\left( {\dfrac{7}{2}} \right)$?

Answer 1

Hint: The given function is a inverse trigonometric function the inverse trigonometric function are inverse function which give the value of a particular degree at which a given trigonometric gives the desired results it is sort of a function that reverses the effect the trigonometric function so the inverse tangent function in this case will reverse the tan function. We have to now find the value of the degree at which the tan function gives the given value inside the brackets. The following functions can be easily calculated on the calculator by using the inverse button given in the calculator but be sure to put radian on the mode selection in case we want value in radians for the given function.

Complete step-by-step answer:
The inverse trigonometric functions are the inverse function of their trigonometric functions and also work as such in the way the inverse function works. We input a value and the function gives us the value of the degree at which the given trigonometric function gives that value. The step by step procedure to find the value of inverse trigonometric function on a scientific calculator is as follows.
Press the button denoting inverse function in the calculator
Then press the value of trigonometric in case given here we select the tan function
 Then input the value of $\dfrac{7}{2}$instead of the the fraction we input $3.5$
The answer will come in the case of degree by default in case we want the answer to be in radian then put radian in the mode to obtain the answer in radian.
The answer in radian will be $1.292496668$ or in case of degree will be \[\;74.0546041\]
So, the correct answer is “$1.292496668$ RADIAN OR \[\;74.0546041\] DEGREES”.

Note: We will pay close attention to whether a question is asked for radian or in degree and then select appropriate option in the calculator accordingly.