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How do you find the exact value of tan(θ)=4 ?

Answer
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Hint: We solve the given problem with the help of a graphing calculator. This is done by pressing the “2ND ” key followed by the “TAN ” key and then the value “ 4 “. After pressing the “ ENTER ” key, we get the answer.

Complete step by step answer:
In the given problem, we have to find the value of θ at which tanθ is 4 . We can do this on a graphical calculator like the TI84 calculator. The TI84 calculator provides a direct program to find the inverse trigonometric functions.
To evaluate the inverse trigonometric functions on TI84 , we at first press the “ 2ND “ key to activate the alternative function of a key. We now press the “ TAN ” key to enter the tan1 function as the “ 2ND ” already activated the inverse operator before. Now, we can either enter a parenthesis or not enter it as both will yield the same answer is this case. We now press the “ ” key followed by pressing the “ 4 “ key to enter 4 .
Having entered all the values, we now press the “ ENTER ” key. After pressing the “ENTER ” key, the calculator immediately presents the answer “ 76.96 ” which is in degrees as the default mode of the calculator for angle measurements in degrees. We can change the settings to radian by pressing the “ MODE ” key.
Now, the range of tan1x is (90,90) and our answer is 76.96 . Therefore, we can conclude that the exact value of tan(θ)=4 is θ=76.96 .

Note:
We should keep mind the range of various trigonometric functions like sin1x,cos1x and should write the answers within that range only. The calculator always shows the answer which is closest to the xaxis and therefore, we should transform these values to the values within range. This problem can also be solved by plotting the graph of tanx and drawing another line y=4 . The point of intersection within the region $\left( -{{90}^{\circ }}