Chapter 13.7, Problem 4CE

a.

To determine

Calculate the value of the given function.

Answer to Problem 4CE

The solution is,

  $\text{sin7}\theta =\text{0}\text{.8910}$

Explanation of Solution

Given:The function is,

  $\text{sin7}\theta$

And,

  $\sin \theta =\text{0}\text{.156422}$

Calculation:

Use sine addition rule,

  $\sin (a+b)=\sin a\cos b+\cos a\sin b$

We may rewrite the function as,

  $\sin (4\theta +3\theta )=\sin 4\theta \cos 3\theta +\cos 4\theta \sin 3\theta$

Then,

  $\text{sin7}\theta =\text{0}\text{.8910}$

program:

function [S] = sine(a,b)
theta=asin(0.156422)*180/pi;
cosd(a)=sqrt(1-sind(a*theta).^2);
cosd(b)=sqrt(1-sind(b*theta).^2);
S=sind(a*theta)*cosd(b)+cosd(a)*sind(b*theta);
end

clc
clear
close all
a=4;b=3;
[S]=sine(a,b)

Query:

• First, define the angles.
• Then calculate value of the $\text{sin7}\theta$ using function “sine”.

b.

To determine

Calculate the value of the given function.

Answer to Problem 4CE

The solution is,

  $\text{sin15}\theta =\text{1}$

Explanation of Solution

Given:The function is,

  $\text{sin7}\theta$

And,

  $\sin \theta =\text{0}\text{.156422}$

Calculation:

Use sine addition rule,

  $\sin (a+b)=\sin a\cos b+\cos a\sin b$

We may rewrite the function as,

  $\sin (8\theta +7\theta )=\sin 8\theta \cos 7\theta +\cos 8\theta \sin 7\theta$

Then,

  $\text{sin15}\theta =\text{1}$

program:

function [S] = sine(a,b)
theta=asin(0.104528)*180/pi;
cosd(a)=sqrt(1-sind(a*theta).^2);
cosd(b)=sqrt(1-sind(b*theta).^2);
S=sind(a*theta)*cosd(b)+cosd(a)*sind(b*theta);
end

clc
clear
close all
a=8;b=7;
[S] = sine(a,b)

Query:

• First, define the angles.
• Then calculate value of the $\text{sin15}\theta$ using function “sine”.