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The curves with equations $ x = \alpha \sin nt $, $ y = b \cos t $ are called Lissajous figures. Investigate how these curves vary when $ a $, $ b $, and $ n $ vary. (Take $ n $ to be a positive integer.)

figures have $n-1$ points of intersection, all of which are on the $y$ -axis, and a total of $n$ closed loops.

Calculus 2 / BC

Chapter 10

Parametric Equations and Polar Coordinates

Section 1

Curves Defined by Parametric Equations

Parametric Equations

Polar Coordinates

Missouri State University

Campbell University

Oregon State University

University of Michigan - Ann Arbor

Lectures

01:11

In mathematics, integratio…

06:55

In grammar, determiners ar…

01:33

The curves with equations …

04:25

Lissajous curves Consider …

03:03

Graph several members of t…

03:07

Lamé curves The Lamé curve…

03:24

00:49

The curves defined by the …

03:00

Use a graphing calculator …

00:53

Compare the curves represe…

00:56

Beautiful curves Consider …

the curves. These equations actually go to eight hands. Signed aunty. Why is he Goto Be Pam's Kasai? Inti A card researchers fingers. You must get how this care Safari, What a B and E and Larry. We can see that when N is equal to to the curve in this act itself at one point and physical to three curves intersect itself at two points. What end is a control? Four. The curve in dissects itself at three points, so we can conclude that. But general thin to curve into sex itself at minus one points. And if a is getting larger and larger with half the wife of the curve, it's catching bigger and bigger. One p is getting larger and larger. Half the laugh off the curve. It's catching bigger and bigger.

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In mathematics, integration is one of the two main operations in calculus, w…

In grammar, determiners are a class of words that are used in front of nouns…

The curves with equations $x=a \sin n t, y=b \cos t$ arecalled Lissajous…

Lissajous curves Consider the following Lissajous curves. Find all points on…

Graph several members of the family of curves $ x = \sin t + \sin nt $, $ y …

Lamé curves The Lamé curve described by $\left|\frac{x}{a}\right|^{n}+\left|…

Graph several members of the family of curves$x=\sin t+\sin n t, y=\cos …

The curves defined by the following parametric equations are from the cycloi…

Use a graphing calculator to experiment with parametric equations of the for…

Compare the curves represented by the parametric equations. How do they diff…

Beautiful curves Consider the family of curves $x=\left(2+\frac{1}{2} \sin a…

06:04

(a) Approximate $ f $ by a Taylor polynomial with degree $ n $ at the number…

01:35

Two graphs, $ a $ and $ b $, are shown. One is a curve $ y = f(x) $ and the …

01:43

Set up an integral that represents the length of the curve. Then use your ca…

04:39

Find $ dy/dx $ and $ d^2y/dx^2 $. For which values of $ t $ is the curve con…

05:05

(a) If a particle moves along a straight line, what can you say about its ac…

02:11

Find $ dy/dx $,

$ x = \dfrac{t}{1 + t} $, $ \quad y = \sqrt{1 + t} $…

00:37

Find the sum of the series.

$ \sum_{n = 0}^{\infty} \frac {3^n}{5^n …

01:34

Find the length of the curve.

$ r(t) = \langle 2t, t^2, \frac{1}{3} …

02:09

$ r(t) = i + t^2 j + t^3 k $ , $ 0 \le…

03:31

If $ r(t) = u(t) \times v(t) $, where $ u $ and $ v $ are the vector functio…

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The number 2 is also the smallest & first prime number (since every other even number is divisible by two).

If you write pi (to the first two decimal places of 3.14) backwards, in big, block letters it actually reads "PIE".

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