Question

Plot the following trig functions using subplots, choosing an appropriate layout for the number of functions displayed. The subplots should include a title which is the equation displayed. The independent variable (angle) should vary from 0 to 360 degrees and the plots should use a solid red line.

Answer 1

The question is incomplete! The complete question along with Matlab code and explanation is provided below.

Question

Plot the following trig functions using subplots, choosing an appropriate layout for the number of functions displayed. The subplots should include a title which is the equation displayed. The independent variable (angle) should vary from 0 to 360 degrees and the plots should use a solid red line.

1. cos(u - 45)

2. 3cos(2u) - 2

3. sin(3u)

4. -2cos(u)

Matlab Code with Explanation:

u=[0:0.01:2*pi] % independent variable represents 0 to 360 degrees in steps of 0.01

y1=cos(2*pi*u-45); % function 1

y2=3*cos(2*pi*2*u)-2;  % function 2

y3=sin(2*pi*3*u);  % function 3

y4=-2*cos(2*pi*u);  % function 4

subplot(4,1,1) % 4 rows, 1 column and at position 1

plot(u,y1,'r');  % this function plots y w.r.t u and 'r' is for red color

grid on   % turns on grids

xlabel('u') % label of x-axis

ylabel('y1')  % label of x-axis

title('y1=cos(2*pi*u-45)') % title of the plot

ylim([-3 3]) % limits of y-axis

xlim([0 2*pi]) % limits of x-axis

% repeat the same procedure for the remaining 3 functions

subplot(4,1,2)

plot(u,y2,'r');  

grid on  

xlabel('u')  

ylabel('y2')  

title('y2=3*cos(2*pi*2*u)-2')  

ylim([-6 3])

xlim([0 2*pi])

subplot(4,1,3)  

plot(u,y3,'r');

grid on  

xlabel('u')  

ylabel('y3')  

title('y3=sin(2*pi*3*u)')  

ylim([-3 3])  

xlim([0 2*pi])

subplot(4,1,4)  

plot(u,y4,'r');  

grid on  

xlabel('u')

ylabel('y4')  

title('y4=-2*cos(2*pi*u)')  

ylim([-3 3])

xlim([0 2*pi])

Output Results:

The first plot shows a cosine wave with a phase shift of 45°

The second plot shows that the amplitude of the cosine wave is increased and the wave is shifted below zero level into the negative y-axis because of -2 also there is a increase in frequency since it is multiplied by 2.

The third plot shows that the frequency of the sine wave is increased since it is multiplied by 3.

The fourth plot shows a cosine wave which is multiplied by -2 and starts from the negative y-axis.