Question

How do you use a calculator to evaluate \[\sec 2.8\]?

Answer 1

Hint: In this question, we want to find the value of the trigonometric sec function that is inverse of cosine using a calculator. Therefore, the steps to find the sec function $\sec x$ using the calculator are as below.

Complete step by step solution:
Make sure we are in the correct mode (radian or degree).
Press the $1$ button.
Press $\div $ button.
Press the $\cos $button.
Enter the value given for angle $x$.
Press [ENTER] or $=$ button.
In this question, we want to find the value of the sec function using a calculator.
Scientific calculators are calculators that are used not only for basic arithmetic, such as addition, subtraction, multiplication, and division, but also for more advanced operations such as exponents, logarithms, scientific notations, and trigonometric functions. But they don’t have graphing capabilities.
While doing our problem, we also need to check the mode of the scientific calculator.
When we are working with trigonometric functions of angles in degrees or radians, we have to make sure that the calculator is working in the same mode.
The sine, cosine, and tangent trigonometric functions will be there on a scientific calculator as the buttons \[\sin ,\cos ,\tan \] respectively.
The first step is to make sure that we are in the correct mode.
In this question, set the calculator in the radian mode.
The second step is to press the $1$ button.
The third step is to press the $\div $ button.
The fourth step is to $\cos $button. (since we are finding $\sec x$ value and that is an inverse of cosine function)
The fifth step is to enter the value given for angle in $\sec $.
In this question, we want to find the sec function at the angle $2.8$.
$\Rightarrow \sec \theta =\dfrac{1}{\cos \theta }$
That is,
$\Rightarrow \sec 2.8=\dfrac{1}{\cos 2.8}$
The last step is to press the “ENTER” button or “$=$” to find the final answer.
On pressing ENTER, we get our answer as:
$\Rightarrow \sec 2.8=1.00119529$

Note: We can also find the cosec and cot functions by following the same steps.
For the function $\csc \left( x \right)$ and $\cot \left( x \right)$ , we will use the SIN and TANGENT function property in place of COSINE.
We can also directly find these inverse trigonometric functions by pressing “shift” and then pressing the trigonometric function button, but with this we can only find the defined degree value of our trigonometric functions.