Supposedly, this is a true statement, but I don't know why. Is there some indentity about cos of half angles and inequalities? The equation displayed in the image is:\[ \cos(\pi t / 2) \leq -\frac{\pi}{2} t + \frac{\pi}{2}. \]This mathematical statement expresses an inequality involving the cosine function and a linear expression. The left-hand side of the inequality is the cosine of \(\pi t / 2\), while the right-hand side is a linear function of \(t\) with a negative slope and a positive y-intercept.### Explanation:- \(\cos(\pi t / 2)\): This is the cosine function, which is being evaluated at \(\pi t / 2\). The cosine function is well-known for its periodic nature and oscillates between -1 and 1.- \(-\frac{\pi}{2} t + \frac{\pi}{2}\): This is a linear function of \(t\). The slope of this line is \(-\frac{\pi}{2}\), and the y-intercept is \(\frac{\pi}{2}\).This inequality shows that for different values of \(t\), the cosine function evaluated at \(\pi t / 2\) is less than or equal to the linear function provided by \(-\frac{\pi}{2}t + \frac{\pi}{2}\).### Graphical Interpretation:If you were to graph both sides of this inequality on a Cartesian coordinate system with \(t\) on the x-axis and \(y\) on the y-axis, you would:- Graph \(\cos(\pi t / 2)\), which is a wave that repeats every 4 units given by the period \(\frac{2\pi}{\pi/2} = 4\). - Graph the linear function \(-\frac{\pi}{2} t + \frac{\pi}{2}\).### Intersection Points:Where the curve of \(\cos(\pi t / 2)\) meets or lies below the line \(-\frac{\pi}{2} t + \frac{\pi}{2}\) are the points that satisfy this inequality.This inequality may have practical applications in various fields such as signal processing, physics, and engineering where wave behavior could be compared with linear transformations.

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Answered: cos(nt/2)

Math

Advanced Math

cos(nt/2)

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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