Question

How do you use a calculator to evaluate \[{{\tan }^{-1}}(-0.2)\] in both radians and degrees?

Answer 1

Hint: The basic inverse trigonometric functions are used to find the missing angles in right triangles. We can use a TI calculator to find the inverse trigonometric values easily. A TI calculator is ideal for students to use in mathematical and scientific studies.

Complete step by step answer:
As per the given question, we have to find the inverse trigonometric value, \[{{\tan }^{-1}}(-0.2)\].

For most TI – Texas Instruments graphing calculators, firstly, we have to press the MODE button which is present on it and we need to select the RADIAN option by pressing down twice. Then, we pressed the ENTER button to put the calculator in radian mode.

When we press the second button, then the MODE button goes back to the normal calculator screen.

When we have pressed the second button, then the TAN button to make the inverse tangent function to appear on the screen where we have to write the value whose inverse tangent value is to be found.

Now, we have to enter \[-0.2\] (since we have to find \[{{\tan }^{-1}}(-0.2)\]) and then we have to close the parenthesis and the screen shows:
\[{{\tan }^{-1}}(-0.2)\].
At this stage, we have to press the ENTER button to get the result required.

Then we have to repeat the same process from the start with DEGREE mode by selecting DEGREE instead of RADIAN after pressing the MODE button.

At the end of each process, we get the following values:
Radians: \[{{\tan }^{-1}}(-0.2)=-0.197\] when rounded to three decimal places.
Degrees: \[{{\tan }^{-1}}(-0.2)=-11.310\] when rounded to three decimal places.

\[\therefore -0.197\] and \[-11.310\] are the required values of \[{{\tan }^{-1}}(-0.2)\] in radians and degrees respectively.

Note:
We can find angle A (using inverse trigonometric functions) with the angle making sides of length b and c, then we can use \[{{\cos }^{-1}}A=\dfrac{b}{c}\]. We know that arctan, arcsine, arccsc, arccot are restricted to quadrant 1 and 4. When we have to find the fourth quadrant, we take it negatively. We should avoid calculation mistakes to get the correct results.