Question

Use a calculator to evaluate the trigonometric function for the indicated value.Round your answer to four decimal places.

Answer 1

Given:

There are given the trigonometric funtion:

$sec(20^{\circ}20^{\prime}18^{\prime}^{\prime})$

Explanation:

According to the question:

First, we need to convert all minutes into degrees.

So,

To find the minute to a degree, we need to divide by 60 degrees.

Then,

$\begin{gathered} 20^{\prime}=\frac{20}{60} \\ =0.33^{\circ} \end{gathered}$

Then,

$1^{\prime}^{\prime}=\frac{1}{60}^{\prime}$

Then,

$\begin{gathered} 18^{\prime}^{\prime}=\frac{18}{60}^{\prime} \\ =0.3^{\prime} \end{gathered}$

Then,

$\begin{gathered} 0.3^{\prime}=\frac{0.3}{60}^{\circ} \\ =0.005^{\circ} \end{gathered}$

So,

The final trigonometric function will be:

$sec(20^{\circ}+0.33^{\circ}+0.005^{\circ})=sec(20.335^{\circ})$

Then,

The value of the given sec function is:

$sec(20.335^{\circ})=\frac{1}{cos(20.335^{\circ)}}$

Then,

$\begin{gathered} sec(20.335^{\operatorname{\circ}})=\frac{1}{cos(20.335^{\operatorname{\circ}})} \\ =\frac{1}{0.9} \\ =1.11 \end{gathered}$

Final answer:

Hence, the value of the given expression is 1.11