Question

Using a scientific calculator, how do you find the measure of the angle whose tangent value is 1.2799?

Answer 1

Calculators are able to determine trigonometric function values in degrees and radians. To find the angle, the calculator is set to Degree mode and 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 solution:
Given,
tangent value = 1.2799; and we need to find the angle of the given tangent.
Converting tangents to degrees requires you to apply the arctan function to the tan of the angle. The following expression shows how to convert tangents to degrees:
Angle in degrees $= \arctan \left( x \right)$ or $ta{n^{ - 1}}\left( x \right)$ as:
Angle in degrees = ${\tan ^{ - 1}}\left( {1.2799} \right) = {52^\circ }$
Using a scientific calculator, to get the tan inverse, it will depend upon your calculator. Look for one of the following: ${\tan ^{ - 1}}$ or $\arctan$.
Typically, this would be a "2nd function" key, simply put, the arctan function reverses the effect of the tan function.
So,
Press the “${\tan ^{ - 1}}$” button to apply the $\arctan$ function
${\tan ^{ - 1}}$ (or whatever is the given function), as given here: ${\tan ^{ - 1}}\left( {1.2799} \right)$
Then press " ENTER " or "=" key.
The inverse value is displayed as ${51.99^\circ } \simeq {52^\circ }$.
On TI-84 calculator,
Enter the inverse trigonometric function of the trigonometric value i.e., given $\tan \left( {1.2799} \right)$ 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 ${\tan ^{ - 1}}\left( {1.2799} \right)$ into degrees, press 2nd and then press Tan. The display will show ${\tan ^{ - 1}}$, or inverse tan. Now enter 1.2799 and a closing parenthesis.
Press ENTER and collect your answer. The result should be a number, expressed in degrees. For example, if you entered ${\tan ^{ - 1}}\left( {1.2799} \right)$ and hit enter, the calculator will display 51.99, which is 52 degrees. Be sure to remember the closing parenthesis.
Hence, in this way we can find the degrees whose tangent value is 1.2799 using a calculator.

Note: The function called $\arctan$or tan−1 reverses the tan function, and returns the original angle when you apply it to the tan of the angle. $\arcsin$ and $\arccos$ do the same thing with the sin and cos functions, respectively. We have used TI-84 as it is capable of going in both directions i.e., from the angle to the trigonometric measure and using a TI-84 Plus calculator you can easily convert the basic trigonometric functions into angles measured in degrees or radians.