Chapter 4.3, Problem 32E

(a)

To determine

The value of $\cos 8°50^{\prime }25^{″}$ using a calculator and round it to four decimal places.

Answer to Problem 32E

The value of $\cos 8°50^{\prime }25^{″}$ is $0.9881$ .

Explanation of Solution

Given:

The trigonometric identity is $\cos 8°50^{\prime }25^{″}$ .

Calculation:

Convert $8°50^{\prime }25^{″}$ into degrees.

  $\begin{array}{c}8°50^{\prime }25^{″}=8°+{\left(\frac{50}{60}\right)}^{°}+{\left(\frac{25}{3600}\right)}^{°}\\ =8°+0.8333°+0.0069°\\ =8.8402°\end{array}$

The value of $\cos 8402°$ 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 $\cos 8402°$ using the calculator is,

  $\cos 8.8402°=0.9881207999$

Round off the answer to four decimal places gives $0.9881$ .

Therefore, $\cos 8°50^{\prime }25^{″}=0.9881$ .

(b)

To determine

The value of $\sec 56°10^{\prime }$ using a calculator and round it to four decimal places.

Answer to Problem 32E

The value of $\sec 56°10^{\prime }$ is $1.7960$ .

Explanation of Solution

Given:

The trigonometric identity is $\sec 56°10^{\prime }$ .

Calculation:

Convert $\sec 56°10^{\prime }$ into degrees.

  $\begin{array}{c}56°10^{\prime }=56°+{\left(\frac{10}{60}\right)}^{°}\\ =56°+0.1666°\\ =56.1666°\end{array}$

The value of $\sec 56.1666°$ 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 $\sec 56.1666°$ using the calculator is,

  $\sec 56.1666°=1.7960417341$

Round off the answer to four decimal places gives $1.7960$ .

Therefore, $\sec 56°10^{\prime }=1.7960$ .