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.

Answered: Image /qna-images/answer/fb59860f-315b-45e1-82ad-43bdd990945e.jpg

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

See similar textbooks

Related questions

Q: Apply the Angle Bisector Theorem to the smallest angle of the right triangle whose sides are 1, 2…

Q: 6. Clara claims "all obtuse triangles are similar." Which statement best describes Clara's claim? A.…

Q: Question 1. Suppose you know that VrVyP(x, y) is true. Which of the following statement (s) must…

A: Given :∀x∀yP(x,y) is true To Check: Which of the following are also true: (i) ∀y∃xP(x,y) is also…

Q: 3 21. Find the roots then graph. use the positive angle only-

A: Cube root of 21 by Halley`s Method Its formula is 3a≈x((x3+2a)/(2x3+a)) Where, a= number of whose…

Q: True or False: An inscribed triangle divides the circle into three arcs, 148°, 200° and 12°, then…

A: Given : A triangle divides the circle into three arcs 148°,200° and 12°

Q: Explain what special right triangles are. Draw an example of each and label the special features.…

A: special right triangles explanation

Q: 5. State the postulate or theorem you can use to prove the pair of triangles congruent.

A: Given, The pair of triangles are shown below : To show : State the postulate…

Q: XYZ is a triangle and YA←→∥XZ←→YA↔∥XZ↔. Prove that the interior angles of a triangle sum to 180180…

Q: ? 14 yd Y 3 yd

A: See attached file for a step by step explanation.

Q: The sum of all the measures of the exterior angles of a triangle is equal to (1) 90 (3) 270° (4) 360…

A: By using triangle property, we measure the sum of exterior angles

Q: e Sun 1° Earth 1 day later f Earth

A: The Earth completes one full rotation, or 360 degrees, every 24 hours. This rotation is what allows…

Q: There are some instances when an abbreviated form of the distance formula can be used. What is the…

A: Please see the below picture for detailed solution.

Q: Find the measures of the angles of a triangle if it is known that the measures are x, 21 – x, and…

Q: 2. Consider the triangle below. M 64 Determine the angle measure for zA and ZM in order for AGAM to…

Q: 23. Place 'A' is 178 m due south of place 'B', place 'C is 273 m away from the place 'A', and 235 m…

A: The possible figure

Q: 17. The reference angle for = -420° is (a) -60° (b) 30° (c) 60° (d) 420° (e) does not exist

A: This question can be solved by looking at the position of the terminal side of the angle.

Q: calculate the lengths of all three sides using the distance formula of the non-right angle triangle…

Q: 28. Line m and line n are parallel. They are intersected by line p as shown. (2x + 70°) (x-10°) m…

A: We have to find angle Q

Q: Use Euler circles to check the validity of the argument: All red hair is pretty. No pretty things…

A: Given argument: All red hair is pretty. No pretty things are valuable, Therefore, no red hair is…

Question

100%

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.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 2 steps with 2 images

SEE SOLUTION Check out a sample Q&A here

Similar questions

4) Given that the three side lengths of an obtuse triangle are three successive positive integers. If is the largest interior angle, find cose. (A) 4 (B) 14 (C) - I e
The symmetric property of equality states that a segment or angle is congruent with itself. True O False
12. The Statue of Liberty is 150 feet tall and stands on a 150 foot pedestal. How far from the base should you stand to have the statue subtend the largest possible angle at your camera lens, assuming the camera is held 5 feet off the ground and the ground is flat? 150 150
You are trying to prove triangle EHI is congruent to triangle FGI. You need to prove that <EIH is congruent to <FIG. What is the reason for this statement?
What is the Pythagorean Theorem in deep detail?
An architect designs a wheelchair ramp for a historical building. The entry way is a level platform at the top of stairs that are 3 meters above ground level and extend 4 m out from the building. There is an obstacle 25 m from the stairs, and the city code for ramps limits the incline angle to 6º. Is there sufficient distance for a ramp within this limit? How do you know? O Yes, because the ratio of O No, because the ratio of O No, because the ratio of is less than tan 6º. is greater than sin 6º. is greater than tan 6º. O Yes, because the ratio of is less than sin 6º.
It is impossible to construct triangles in Elliptic Geometry. True False
Which value of X could sow that <2 and <6 are corresponding angle? And why?
If n represents any integer, then an expression representing all angles coterminal with 120° is 120° + If n represents any integer, then an expression representing all angles coterminal with 120° is 120° + (Type an equation using n as the variable.)
Prove the statement in incidence geometry. Restate and explain each step of the proof. -> Every point lies on two distinct lines.