Chapter 4.3, Problem 39E

(a)

To determine

To find: The value of given function using the calculator.

Answer to Problem 39E

The value of $\csc 32°40\text{'}3\text{'}\text{'}=\csc 32\cdot 6675°$ , to four places is $1\cdot 08527$ .

Explanation of Solution

Given information:

The given function is $\csc 32°40\text{'}3\text{'}\text{'}$ .

Calculation:

Convert the angle to decimal degree using the following relation.

  $1\text{'}=\left(\frac{1}{60}\right)°$ and $1\text{'}\text{'}=\left(\frac{1}{3600}\right)°$

Calculate the value of $32°40\text{'}3\text{'}\text{'}$ .

  $\begin{array}{c}32°40\text{'}3\text{'}\text{'}=32°+\left(\frac{40}{60}\right)°+\left(\frac{3}{3600}\right)°\\ =32\cdot 6675°\end{array}$

Now the angle is in degree.

Calculate the value of $\csc 32\cdot 6675°$ using calculator.

Set the mode of the calculator to degree mode.

As we know that cosecant is the reciprocal function of the sine function.

The calculator keystrokes as follows.

  $\boxed{(}\boxed{\text{SIN}}\boxed{(}32\cdot 6675\boxed{)}\boxed{)}\boxed{x^{-1}}\boxed{\text{ENTER}}$

The answer displayed on the calculator is $1\cdot 08527$ .

Therefore, the value of $\csc 32°40\text{'}3\text{'}\text{'}=\csc 32\cdot 6675°$ , to four places is $1\cdot 08527$ .

(b)

To determine

To find:The value of given function using the calculator.

Answer to Problem 39E

The value of $\tan 44°28\text{'}16\text{'}\text{'}=\tan 44.4711°$ , to four places is $0\cdot 9817$ .

Explanation of Solution

Given information:

The given function is $\tan 44°28\text{'}16\text{'}\text{'}$ .

Calculation:

Convert the angle to decimal degree using the following relation.

  $1\text{'}=\left(\frac{1}{60}\right)°$ and $1\text{'}\text{'}=\left(\frac{1}{3600}\right)°$

Calculate the value of $44°28\text{'}16\text{'}\text{'}$ .

  $\begin{array}{c}44°28\text{'}16\text{'}\text{'}=44°+\left(\frac{28}{60}\right)°+\left(\frac{16}{3600}\right)°\\ =44\cdot 4711°\end{array}$

Now, the angle is in degree.

Set the mode of the calculator to degree mode.

The calculator keystrokes as follows.

  $\boxed{\text{TAN}}\boxed{(}44\cdot 4711\boxed{)}\boxed{\text{ENTER}}$

The answer displayed on the calculator is $0\cdot 9817$ .

Therefore, the value of $\tan 44°28\text{'}16\text{'}\text{'}=\tan 44.4711°$ , to four places is $0\cdot 9817$ .