I am trying to find 4 parameters as shown in the image. I started the MATLAB code but I don't have an idea of how the find the parameters. Can you help me find the four parameters for each i. The following is my code: clc;clear all;i = 1:50;theta = zeros(size(i));lambda_hat = [1/sqrt(3); 1/sqrt(3); 1/saqrt(3)];for i = 1:50 theta(i) = pi + (10^-6)*randn(1); endi = 1:50;semilogy(i,theta) The image shows a mathematical expression involving a vector and trigonometric functions. It is presented as follows:\[\epsilon^{(i)} = \begin{bmatrix}\epsilon_{1:3}^{(i)} \\\epsilon_4^{(i)}\end{bmatrix}=\begin{bmatrix}\hat{\lambda} \sin(\theta^{(i)}/2) \\\cos(\theta^{(i)}/2)\end{bmatrix}\]Explanation:- \(\epsilon^{(i)}\) represents a vector indexed by \(i\).- \(\epsilon_{1:3}^{(i)}\) and \(\epsilon_4^{(i)}\) are components of this vector.- The right side of the equation expresses these components in terms of trigonometric functions: - The first element is \(\hat{\lambda} \sin(\theta^{(i)}/2)\), where \(\hat{\lambda}\) is a unit vector multiplied by the sine of half the angle \(\theta^{(i)}\). - The second element is \(\cos(\theta^{(i)}/2)\), which is the cosine of half the angle \(\theta^{(i)}\).This vector representation is often encountered in fields such as physics or engineering, particularly in discussions of rotations or transformations.

Clear the MATLAB workspace and command window.Create an array i from 1 to 50.Initialize arrays…

Answered: I am trying to find 4 parameters as…

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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I am trying to find 4 parameters as shown in the image. I started the MATLAB code but I don't have an idea of how the find the parameters. Can you help me find the four parameters for each i. The following is my code:

clc;
clear all;

i = 1:50;
theta = zeros(size(i));
lambda_hat = [1/sqrt(3); 1/sqrt(3); 1/saqrt(3)];

for i = 1:50

theta(i) = pi + (10^-6)*randn(1);

end

i = 1:50;
semilogy(i,theta)

The image shows a mathematical expression involving a vector and trigonometric functions. It is presented as follows:

\[
\epsilon^{(i)} =
\begin{bmatrix}
\epsilon_{1:3}^{(i)} \\
\epsilon_4^{(i)}
\end{bmatrix}
=
\begin{bmatrix}
\hat{\lambda} \sin(\theta^{(i)}/2) \\
\cos(\theta^{(i)}/2)
\end{bmatrix}
\]

Explanation:

- \(\epsilon^{(i)}\) represents a vector indexed by \(i\).
- \(\epsilon_{1:3}^{(i)}\) and \(\epsilon_4^{(i)}\) are components of this vector.
- The right side of the equation expresses these components in terms of trigonometric functions:
- The first element is \(\hat{\lambda} \sin(\theta^{(i)}/2)\), where \(\hat{\lambda}\) is a unit vector multiplied by the sine of half the angle \(\theta^{(i)}\).
- The second element is \(\cos(\theta^{(i)}/2)\), which is the cosine of half the angle \(\theta^{(i)}\).

This vector representation is often encountered in fields such as physics or engineering, particularly in discussions of rotations or transformations.

Expert Solution

Step 1: Algorithm:

Clear the MATLAB workspace and command window.
Create an array i from 1 to 50.
Initialize arrays theta, lambda, theta_half, sin_theta_half, and cos_theta_half, all of the same size as i, to store the parameters.
Loop over each element in the array i: a. Generate a random value for theta(i) with a small amount of Gaussian noise. b. Calculate lambda(i) as 1 divided by the square root of 3. c. Calculate theta_half(i) as half of the value of theta(i). d. Calculate sin_theta_half(i) as the sine of theta_half(i). e. Calculate cos_theta_half(i) as the cosine of theta_half(i).
Plot the theta values using a semilogarithmic scale.
Display the parameters in a tabular format, showing i, lambda, theta_half, sin_theta_half, and cos_theta_half for each i.

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