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Graph several members of the family of curves with parametric equations $ x = t + \alpha \cos t $, $ y = t + \alpha \sin t $, where $ \alpha > 0 $. How does the shape change as $ \alpha $ increases? For what values of $ \alpha $ does the curve have a loop?

$(3),$ we get $a=\frac{\sqrt{2}\left(\frac{3 \pi}{4}-t\right)}{\sin \left(\frac{3 \pi}{4}-t\right)} .$ Write $z=\frac{3 \pi}{4}-t .$ Then $a=\frac{\sqrt{2} z}{\sin z},$ where $z>0 .$ Now $\sin z<z$ for $z>0,$ so $a>\sqrt{2}$$\left[\mathrm{As} z \rightarrow 0^{+}, \text {that is, as } t \rightarrow\left(\frac{3 \pi}{4}\right)^{-}, a \rightarrow \sqrt{2}\right]$GRAPH

Calculus 2 / BC

Chapter 10

Parametric Equations and Polar Coordinates

Section 1

Curves Defined by Parametric Equations

Parametric Equations

Polar Coordinates

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Lectures

01:11

In mathematics, integratio…

06:55

In grammar, determiners ar…

01:43

Graph several members of t…

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Investigate the family of …

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03:14

(a) Investigate the family…

03:44

A family of curves is give…

02:30

Graphs of Parametric Equat…

01:24

Graph the family of polar …

the problem is Graff, several members of the family of Of Curves with Parametric Equations, Mexico to keep us off our Pam's Kasai Inti. Why is it called T pass off? Our time scientist wire are far is greatest and cereal. How does the shape change? As AF eyeing quizzes, what values of often does a curve half a loop from the graph? We can see that when a is great Hassan one point, or about one point four. So Curve has a loop Onda, but a increases my half. I increases the lube. It's getting larger on DH larger.

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…

Graph several members of the family of curves with parametric equations $x=t…

Investigate the family of curves defined by the parametric equations $ x = t…

Investigate the family of curves defined by the parametricequations $x=t…

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

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

Investigate the family of polar curves$$ r = 1 + \cos^n \theta $$whe…

(a) Investigate the family of curves defined by the polar equations $r=\sin …

A family of curves is given by the equations$r=1+c \sin n \theta,$ where…

Graphs of Parametric Equations Sketch the curve given by the parametric equa…

Graph the family of polar equations $r=1+c \sin 2 \theta$ for $c=0.3,0.6,1,1…