Chapter 4.3, Problem 22E

To determine

To calculate:The missing values in the table by constructing a triangle.

Answer to Problem 22E

The complete table is as follows.

Function	$\theta$ (deg)	$\theta$ (rad)	Function Value
cos	$60°$	$\frac{\pi }{3}$	$\frac{1}{2}$

Explanation of Solution

Given information:

The given table is as follows.

Function	$\theta$ (deg)	$\theta$ (rad)	Function Value
cos	$60°$

Calculation:

Since, the angle is $60°$ and the sum of the internal angles of a triangle is $180°$ . So, the other internal angles of the triangle would be $30°$ and $90°$ .

Calculate the value of $\cos 60°$ .

  $\cos 60°=\frac{1}{2}$

From the above, From the above, it is clear that the internal angles are $30°,60°$ and $90°$ . The opposite side is $\sqrt{3}$ and the hypotenuse is 2. The value of base is 1. Draw a triangle

  

Convert the angle into radians.

  $\begin{array}{c}\text{Radians}=60°\times \frac{\pi }{180°}\\ =\frac{\pi }{3}\end{array}$

The complete table is as follows.

Function	$\theta$ (deg)	$\theta$ (rad)	Function Value
$\cos$	$60°$	$\frac{\pi }{6}$	$\frac{1}{2}$

Therefore, the complete is shown above.