Chapter 13.7, Problem 1CE

To determine

Calculate the value of the angle using sine addition formula.

Answer to Problem 1CE

The solution is,

  

Explanation of Solution

Given:The sine addition formula is,

  $\sin 10°=\sin (5°+5°)=\sin 5°\cos 5°+\cos 5°\sin 5°$

And the value of $\sin 5°$ is,

  $\sin 5°=0.087155743$

Calculation:

Let’s take the angles,

  $angle=5°,10°,15°,20°,25°,30°,35°,40°,45°,50°,55°,60°,65°,70°,75°,80°,85°,90°$

Then use sine addition rule,

  $\sin 10°=\sin (5°+5°)=\sin 5°\cos 5°+\cos 5°\sin 5° \mathrm{......}(1)$

Calculate the $\cos 5°$ ,

  $\cos 5°=\sqrt{1-{\sin }^{2}5°}$

Put the value of $\cos 5°$ into the equation (1) then,

  $\sin 10°=\text{0}\text{.17365}$

Then repeat the same process for all the angles.

program:

function S = sinadd(a,b)
% funtion for sin(a+b)
cosd(a)=sqrt(1-sind(a).^2);
cosd(b)=sqrt(1-sind(b).^2);
S=sind(a)*cosd(b)+cosd(a)*sind(b);
end

clc
clear
close all
a=5; b=(10:5:90)-a;
fori=1:17
    S=sinadd(a,b(i));
    sol(i)=S;
end
value=sol';
angle=(a+b)';
T = table(angle,value)

Query:

• First, define the angles.
• Then calculate value of each angle using function “sinadd”.
• Then convert into tabulate form.