Chapter 5.2, Problem 24E

(a)

To determine

To find: The value of $\sin {52}^{\circ }47\text{'}$ trigonometric ratio, using a calculator.

Answer to Problem 24E

  $\sin {52}^{\circ }47\text{'}=0.79635$

Explanation of Solution

Given information: $\sin {52}^{\circ }47\text{'}$

Calculation:

If you can type minutes as well in the calculator, then simply put the value in to the calculator and get it.

If it is not possible convert the minute to decimal and write the value only in degrees and enter the value in to the calculator.

  $47\text{'}=\frac{{47}^{\circ }}{60}=0.7833$

Hence the value to be entered is ${52.7833}^{\circ }$

Thus,

  $\sin {52}^{\circ }47\text{'}=0.79635$

(b)

To determine

To find: The value of $\cos {79}^{\circ }15\text{'}$ trigonometric ratio, using a calculator.

Answer to Problem 24E

  $\cos {79}^{\circ }15\text{'}=0.1865$

Explanation of Solution

Given information: $\cos {79}^{\circ }15\text{'}$

Calculation:

If you can type minutes as well in the calculator, then simply put the value in to the calculator and get it.

If it is not possible convert the minute to decimal and write the value only in degrees and enter the value in to the calculator.

  $15\text{'}=\frac{{15}^{\circ }}{60}=0.25$

Hence the value to be entered is ${79.25}^{\circ }$

Hence,

  $\cos {79}^{\circ }15\text{'}=0.1865$

(c)

To determine

To find: The value of $\tan {88}^{\circ }22\text{'}45\text{'}\text{'}$ trigonometric ratio, using a calculator.

Answer to Problem 24E

  $\tan {88}^{\circ }22\text{'}45\text{'}\text{'}=35.3401$

Explanation of Solution

Given information: $\tan {88}^{\circ }22\text{'}45\text{'}\text{'}$

Calculation:

If you can type minutes as well in the calculator, then simply put the value in to the calculator and get it.

If it is not possible convert the minute to decimal and write the value only in degrees and enter the value in to the calculator.

  $22\text{'}=\frac{{22}^{\circ }}{60}=0.3333\text{ and 45'}\text{'}=\frac{{45}^{\circ }}{3600}=0.0125$

Hence the value to be entered is ${88}^{\circ }+{0.3667}^{\circ }+{0.0125}^{\circ }={88.3458}^{\circ }$

When you use the above value, you’ll get 35.34087 as the answer due to the round of error in calculating 11/33 in above step. But the correct value is given below.

Thus,

  $\tan {88}^{\circ }22\text{'}45\text{'}\text{'}=35.3401$

(d)

To determine

To find: The value of $\cot {36}^{\circ }$ trigonometric ratio, using a calculator.

Answer to Problem 24E

  $\cot {36}^{\circ }=1.3765$

Explanation of Solution

Given information: $\cot {36}^{\circ }$

Calculation:

  $\begin{array}{l}\cot {36}^{\circ }=\frac{1}{\tan {36}^{\circ }}\\ \cot {36}^{\circ }=\frac{1}{0.7265}\\ \cot {36}^{\circ }=1.3765\end{array}$