Chapter 4.3, Problem 31E

(a)

To determine

Thevalue of $\sec 42°12^{\prime }$ using a calculator and round it to four decimal places.

Answer to Problem 31E

The value of $\sec 42°12^{\prime }$ is $1.3499$ .

Explanation of Solution

Given:

The trigonometric identityis $\sec 42°12^{\prime }$ .

Calculation:

Convert $42°12^{\prime }$ into degrees.

  $\begin{array}{c}42°12^{\prime }=42°+{\left(\frac{12}{60}\right)}^{°}\\ =42°+0.2°\\ =42.2°\end{array}$ .

The value of $\sec 42.2°$ can be calculated by graphical calculator.

Steps to calculate the values using a graphical calculator is as follows.

1. Start calculator and press the “Y” button to enter the function screen.
2. Type the trigonometric function to calculate its value.
3. Press “Enter” to show the result.

So, the value of $\sec 42.2°$ using the calculator is,

  $\sec 42.2°=1.3498836333$

Round off the answer to four decimal places gives $1.3499$ .

Therefore, $\sec 42°12^{\prime }=1.3499$ .

(b)

To determine

The value of $\csc 48°7^{\prime }30^{″}$ using a calculator and round it to four decimal places.

Answer to Problem 31E

The value of $\csc 48°7^{\prime }30^{″}$ is $1.3430$ .

Explanation of Solution

Given:

The trigonometric identity is $\csc 48°7^{\prime }30^{″}$ .

Calculation:

Convert $48°7^{\prime }30^{″}$ into degrees.

  $\begin{array}{c}48°7^{\prime }30^{″}=48°+{\left(\frac{7}{60}\right)}^{°}+{\left(\frac{30}{3600}\right)}^{°}\\ =48°+0.11666°+0.00833°\\ =48.1250°\end{array}$

The value of $\csc 48.1250°$ can be calculated by graphical calculator.

Steps to calculate the values using a graphical calculator is as follows.

4. Start calculator and press the “Y” button to enter the function screen.
5. Type the trigonometric function to calculate its value.
6. Press “Enter” to show the result.

So, the value of $\csc 48.1250°$ using the calculator is,

  $\csc 48.1250°=1.342997774$

Round off the answer to four decimal places gives $1.3430$ .

Therefore, $\csc 48°7^{\prime }30^{″}=1.3430$ .