How do you use a calculator to evaluate $\cos 78^\circ 11'58''$?

Answer

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Hint: Here, we want to find the value of $\cos 78^\circ 11'58''$ by using the calculator. First, let us understand the meaning of $\cos 78^\circ 11'58''$. That is 78 degrees 11 minutes and 58 seconds. Here, we will convert minutes and seconds into degrees. Then take the calculator and set it in degree mode. After that, find the value of $\cos 78^\circ 11'58''$.

Complete step-by-step answer:

By using a calculator, we want to calculate $\cos 78^\circ 11'58''$, we will first convert 11 minutes and 58 seconds to the degrees.

First, let us convert 11 minutes.

11 minutes =$\dfrac{{11}}{{60}}$degrees.

It is also written as,

$ \Rightarrow 11' = 0.1833$

Hence, we can say that 11’ is 0.1833 degrees.

Now, let us convert 58 seconds.

58 seconds =$\dfrac{{58}}{{3600}}$degrees.

It is also written as,

$ \Rightarrow 58'' = 0.0161$

Hence, we can say that 58” is 0.0161 degrees

Now, substitute the value of 11’58” in $\cos 78^\circ 11'58''$.

$ \Rightarrow \cos 78^\circ 11'58'' = \cos (78+0.1833+0.0161)^\circ$

$ \Rightarrow \cos 78^\circ 11'58'' = \cos (78.1994)^\circ$

Now, take a calculator and find the above value.

The calculator gives,

$ \Rightarrow \cos (78.1994)^\circ = 0.2045$

Hence, the answer is 0.2045.

Note:

Calculators are able to determine trigonometric function value in degrees and radians. However, most calculators cannot return the values in radical form. Most will return decimal approximations unless the values are rational. The calculators are two types : Casio and Canon.

Steps to find the value by using the calculator:

> Test the mode that is in degrees or radians.

> Find the mode switcher

> Make sure that the calculator is in degree mode.

> Solve for sides i.e. multiply and divide or solve for angles i.e. inverse.

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