Chapter 4.3, Problem 29E

To determine

The missing values by construction of an appropriate triangle.

Answer to Problem 29E

Table is

Function	$\theta (\mathrm{deg})$	$\theta (rad)$	Function value
cot	${45}^0$	$\frac{\pi }{4}$	$1$

Explanation of Solution

Given information:

A Table is given as

Function	$\theta (\mathrm{deg})$	$\theta (rad)$	Function value
cot			$1$

Formula used:

  $\begin{array}{l}\text{Angle in radian = Angle in degree }\times \frac{\pi }{180}\\ \text{Angle in degree = Angle in radian}\times \frac{180}{\pi }\end{array}$

And

  ${\text{Hypotenuse}}^{\text{2}}{\text{=Base}}^{\text{2}}{\text{+Perpendicular}}^{\text{2}}$

Calculation:

Now, consider

The right-angled triangle is

Using Pythagorean theorem

  $\begin{array}{l}{\text{Hypotenuse}}^{\text{2}}{\text{=Base}}^{\text{2}}{\text{+Perpendicular}}^{\text{2}}\\ {\text{Hypotenuse}}^{\text{2}}=1^{\text{2}}+1^{\text{2}}\\ \text{Hypotenuse}=\sqrt{2}\end{array}$

Therefore, the angle is ${45}^0$ .

Now, find angle in radians

  $\begin{array}{l}\text{Angle in radian = Angle in degree }\times \frac{\pi }{180}\\ \text{Angle in radian = 45}\times \frac{\pi }{180}\\ \text{Angle in radian =}\frac{\pi }{4}\end{array}$

So, table is

Function	$\theta (\mathrm{deg})$	$\theta (rad)$	Function value
cot	${45}^0$	$\frac{\pi }{4}$	$1$