Question

How do you use a calculator to evaluate ${{\cos }^{-1}}0.24$ in both radians and degrees?

Answer 1

In this question we will use the scientific calculator to evaluate the given expression by setting up the calculator in both degrees and radians and evaluating the solution. So, first we must find the answer in degrees as it is default settings and then change the same to radian mode.

Complete step-by-step answer:
We have the expression given to us as:
${{\cos }^{-1}}0.24$
Now while using any TI calculator, it is to be remembered that the calculator will be either in one of the modes while doing any trigonometric operation. It is to be always checked before doing any operation as it will give errors in the solution.
The way to check whether the calculator in degree or radians is through the indicator in the top of the calculator screen which will have an indication as $R$ or $D$ which denotes that the calculator is in radians or degrees respectively.
Now to evaluate ${{\cos }^{-1}}0.24$ in degrees we will first press the shift button and then press the setup button to get into the setup menu of the calculator and then press the number which says $Deg$, which stands for degrees.
Then on using the inverse $\cos$function in the calculator and substituting the value, we get:
$\Rightarrow {{\cos }^{-1}}0.24={{76.113}^{\circ }}$
The above solution is in radians, we will follow the same steps to go in the setup menu, and then press the number which says $Rad$, which stands for degrees.
Then on using the inverse $\cos$function in the calculator and substituting the value, we get:
$\Rightarrow {{\cos }^{-1}}0.24=1.3284$
Which are the required solutions.

Note: It is to be noted that different calculators have different setup functionalities, but the final solution in degree and radians will be the same.
The general degree to radian conversion should be remembered that $1$ radian is equal to approximate $57.2958$.