2.2 Write a MATLAB program to plot the expression y(t) = 2sin?(t) + 8cos(t) – 12. Given t = 0:0.01:2*pi. Attach code and plot screenshot.

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### MATLAB Exercise: Plotting Trigonometric Expressions

**Objective:**
Learn how to write a MATLAB program to plot the expression:

\[ y(t) = 2\sin^2(t) + 8\cos(t) - 12 \]

**Instructions:**
1. **Define the function:** Start by expressing \( y(t) \) in terms of `sin` and `cos` functions in MATLAB.
2. **Specify the range:** Use the provided range for \( t \), which is from 0 to \( 2\pi \) with an increment of 0.01.
3. **Plot the function:** Utilize MATLAB's plotting functions to visualize the expression.

**MATLAB Code Structure:**
```matlab
% Define the range for t
t = 0:0.01:2*pi;

% Calculate y(t) for the given expression
y = 2*sin(t).^2 + 8*cos(t) - 12;

% Plot the function
plot(t, y);
xlabel('t'); % Label for x-axis
ylabel('y(t)'); % Label for y-axis
title('Plot of y(t) = 2sin^2(t) + 8cos(t) - 12'); % Title of the plot
grid on; % Display grid
```

**Graph Explanation:**
- **x-axis (t):** Represents the time variable from 0 to \( 2\pi \).
- **y-axis (y(t)):** Represents the calculated values of the function \( y(t) \).
- **Plot Characteristics:**
  - The graph is continuous and oscillates based on the trigonometric nature of the functions involved.
  - The shape and peaks of the graph are influenced by the sine squared term and the linear cosine term.

This exercise helps in understanding the plotting capabilities of MATLAB and offers insight into how trigonometric functions behave over a specified range. The use of `grid on` facilitates a better analysis of function behavior.
Transcribed Image Text:### MATLAB Exercise: Plotting Trigonometric Expressions **Objective:** Learn how to write a MATLAB program to plot the expression: \[ y(t) = 2\sin^2(t) + 8\cos(t) - 12 \] **Instructions:** 1. **Define the function:** Start by expressing \( y(t) \) in terms of `sin` and `cos` functions in MATLAB. 2. **Specify the range:** Use the provided range for \( t \), which is from 0 to \( 2\pi \) with an increment of 0.01. 3. **Plot the function:** Utilize MATLAB's plotting functions to visualize the expression. **MATLAB Code Structure:** ```matlab % Define the range for t t = 0:0.01:2*pi; % Calculate y(t) for the given expression y = 2*sin(t).^2 + 8*cos(t) - 12; % Plot the function plot(t, y); xlabel('t'); % Label for x-axis ylabel('y(t)'); % Label for y-axis title('Plot of y(t) = 2sin^2(t) + 8cos(t) - 12'); % Title of the plot grid on; % Display grid ``` **Graph Explanation:** - **x-axis (t):** Represents the time variable from 0 to \( 2\pi \). - **y-axis (y(t)):** Represents the calculated values of the function \( y(t) \). - **Plot Characteristics:** - The graph is continuous and oscillates based on the trigonometric nature of the functions involved. - The shape and peaks of the graph are influenced by the sine squared term and the linear cosine term. This exercise helps in understanding the plotting capabilities of MATLAB and offers insight into how trigonometric functions behave over a specified range. The use of `grid on` facilitates a better analysis of function behavior.
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