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

Question

asked Jul 2, 2023 181k views

1 Answer

Zpasternack · Answer 1 · 2023-07-07T08:08:22+0000

Given:

There are given the trigonometric funtion:

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

Step-by-step 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,

$\begin{gathered} 20^(\prime)=(20)/(60) \\ =0.33^(\circ) \end{gathered}$

Then,

$1^(\prime)^(\prime)=(1)/(60)^(\prime)$

Then,

$\begin{gathered} 18^(\prime)^(\prime)=(18)/(60)^(\prime) \\ =0.3^(\prime) \end{gathered}$

Then,

$\begin{gathered} 0.3^(\prime)=(0.3)/(60)^(\circ) \\ =0.005^(\circ) \end{gathered}$

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:

$sec(20.335^(\circ))=(1)/(cos(20.335^(\circ)))$

Then,

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

Final answer:

Hence, the value of the given expression is 1.11