Chapter 9.1, Problem 48E

(a)

To determine

To find: The adjacent to $\theta$ .

Answer to Problem 48E

The adjacent to $\theta$ is $x$ .

Explanation of Solution

Given figure:

  

Calculation:

Consider the figure:

  

The objective is to determine the adjacent side to $\theta$ .

From the figure, observe that the adjacent side to $\theta$ is $x$ .

(b)

To determine

To find: The opposite side of $\theta$ .

Answer to Problem 48E

The opposite side to $\theta$ is $y$ .

Explanation of Solution

Given figure:

  

Calculation:

Consider the figure:

  

The objective is to determine the opposite side of $\theta .$

From the given figure, observe that the opposite side to $\theta$ is $y$ .

(c)

To determine

To find: Weather the function is true and false..

Answer to Problem 48E

The $\cos \theta =\sin ({90}^0-\theta )$ is true.

Explanation of Solution

Given figure:

The given function is $\cos \theta =\sin ({90}^0-\theta )$ .

  

Calculation:

Consider the figure:

  

The objective is to determine whether $\cos \theta =\sin ({90}^0-\theta )$ .

From the formula of $\cos \theta .$ ,

  $\begin{array}{c}\cos \theta =\frac{\text{Adjacent side}}{\text{Hypotenuse }}\\ =\frac{x}{h}\end{array}$

In the view of ${90}^0-\theta$ ,

  $\begin{array}{c}\sin ({90}^0-\theta )=\frac{\text{Opposite side}}{\text{Hypotenuse}}\\ =\frac{x}{h}\end{array}$

Therefore, $\cos \theta =\sin ({90}^0-\theta )$ is true.