Question

How do you use a calculator to evaluate ${\cos ^{ - 1}}\left( { - 0.6} \right)$ in both radians and degrees?

Answer 1

Hint : As we know that the above given function is an inverse trigonometric function. These are the inverse functions of some basic trigonometric functions such as sine, cosine, tangent, secant, cotangent and cosecant. These are also known as arcus function, ant trigonometric function or cyclomatic function. These 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.

Complete step-by-step answer :
According to the given question we have to find the inverse trigonometric value, ${\cos ^{ - 1}}( - 0.6)$ .
Now for the most TI Texas Instruments that are graphing calculators we have to press the MODE button first which is present on it and then we need to select the RADIAN option by pressing it twice and after that we press 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.
In the same way when we press the second button, then the COS button which makes the inverse tangent function to appear on the screen where we write the value whose inverse cos function is to be found.
Now we put $- 0.6$ and it appears in the calculator screen, then we press ${\cos ^{ - 1}}$ (arc sine) . It displays the value which is ${126.68698976^ \circ }$ decimal degrees. We can also write it as .
For radian part $126.68698976 \times \dfrac{\pi }{{180}} = 126.68698976 \times 0.017453292$ , It gives the value $2.2143$ in radians.
Hence the answer is in degrees and $2.2143$ in radian.

Note : We can find any angle using inverse trigonometric functions with the angle making sides of length $b$ and $c$ then we can use the inverse cosine formula ${\cos ^{ - 1}}A = \dfrac{b}{c}$ . We know that arcsine, arccot are restricted to quadrant $1$ . We should always avoid calculation mistakes to get the correct results.