Chapter 14.3, Problem 33PPS

(a)

To determine

To Find: The complete table.

Answer to Problem 33PPS

The required table is shown in Table 2

Explanation of Solution

Given:

The given equation is,

  $\sin \left(A+B\right)=\sin A+\sin B$

The given table is shown in Table 1

Table 1

A(degree)	B(degree)	$\sin A$	$\sin B$	$\sin \left(A+B\right)$	$\sin A+\sin B$
30	90
45	60
60	45
90	30

Calculation:

The completed table is shown in Table 1

Table 2

A(degree)	B(degree)	$\sin A$	$\sin B$	$\sin \left(A+B\right)$	$\sin A+\sin B$
30	90	$\frac{1}{2}$	1	$\frac{\sqrt{3}}{2}$	$\frac{1}{2}+1=\frac{3}{2}$
45	60	$\frac{1}{\sqrt{2}}$	$\frac{\sqrt{3}}{2}$	$\frac{1+\sqrt{3}}{2\sqrt{2}}$	$\frac{2+\sqrt{6}}{2\sqrt{2}}=1.573$
60	45	$\frac{\sqrt{3}}{2}$	$\frac{1}{\sqrt{2}}$	$\frac{1+\sqrt{3}}{2\sqrt{2}}$	$\frac{2+\sqrt{6}}{2\sqrt{2}}=1.573$
90	30	$1$	$\frac{1}{2}$	$\frac{\sqrt{3}}{2}$	$\frac{1}{2}+1=\frac{3}{2}$

(b)

To determine

To Find: The graph for $y=\sin \left(x+x-15\right)$ and $y=\sin x+\sin \left(x-15\right)$ when B is always 15.

Answer to Problem 33PPS

The required graph is shown in Figure 2

Explanation of Solution

Calculation:

Consider the function is,

  $\begin{array}{l}y=\sin \left(x+x-15\right)\\ y=\sin x+\sin \left(x-15\right)\end{array}$

Enter the equation in the graph by pressing Y= as shown in Figure 1

  

Figure 1

Press the graph key the graph of the two function as shown in Figure 2

  

Figure 2

(c)

To determine

To Find: The given function is $\cos \left(A+B\right)=\cos A+\cos B$ .

Answer to Problem 33PPS

The required value is $1.573$ so the identity is not true.

Explanation of Solution

Calculation:

Consider the function is $\cos \left(A+B\right)=\cos A+\cos B$ then,

  $\begin{array}{c}\cos \left(30°+45°\right)=\cos 75°\\ =\frac{\sqrt{3}}{2}+\frac{1}{2}\\ =0.866+0.707\\ =1.573\end{array}$

Since, the value of the cosine function cannot be greater than so the above identity does not hold true.