💬 👋 We’re always here. Join our Discord to connect with other students 24/7, any time, night or day.Join Here!

Like

Report

Get the answer to your homework problem.

Try Numerade Free for 7 Days

Find parametric equations for the parth of a particle that moves along the circle $ x^2 + (y - 1)^2 = 4 $ in the manner described.(a) Once around clockwise, starting at $ (2, 1) $.(b) Three times around counterclockwise, starting at $ (2, 1) $.(c) Halfway around counterclockwise, starting at $ (0, 3) $.

(a) To get a clockwise orientation, we could change the equations to $x=2 \cos t, y=1-2 \sin t, 0 \leq t \leq 2 \pi$(b) To get three times around in the counterclockwise direction, we use the original equations $x=2 \cos t, y=1+2 \sin t$ withthe domain expanded to $0 \leq t \leq 6 \pi$(c) To start at (0,3) using the original equations, we must have $x_{1}=0 ;$ that is, $2 \cos t=0 .$ Hence, $t=\frac{\pi}{2} .$ So we use$x=2 \cos t, y=1+2 \sin t, \frac{\pi}{2} \leq t \leq \frac{3 \pi}{2}$Alternatively, if we want $t$ to start at $0,$ we could change the equations of the curve. For example, we could use$x=-2 \sin t, y=1+2 \cos t, 0 \leq t \leq \pi$

Calculus 2 / BC

Chapter 10

Parametric Equations and Polar Coordinates

Section 1

Curves Defined by Parametric Equations

Parametric Equations

Polar Coordinates

David C.

April 9, 2019

Hi, I was wondering about your thought process in knowing that x=cos(t) and y=2sin(t)+1?

Missouri State University

Harvey Mudd College

Idaho State University

Lectures

01:11

In mathematics, integratio…

06:55

In grammar, determiners ar…

06:12

Find parametric equations …

04:26

01:33

02:03

01:32

03:40

02:22

Circles Find parametrizati…

02:38

04:33

Consider the following par…

01:56

Parametric Equations for C…

The problem is on the parametric equations for the past of a particle that moves along the circle X squared plus y moments. One scribe in secret was four and the minor Describe it or a twice around clockwise starting at to one. Oh aye, we cannot axe is a connective call sign He Why is a call to the selective two times cause Santy, why is it true? Truth? I nti a swan that he is between next to Hi No hi b three dances around and counter clockwise starting at to one. Become like actually go to To Kasai Inti why is they could to sign? He last one t It's between cereal too. Hi. Hot scene halfway around under clockwise starting at zero three. So we can like access to Kasai. Inti Why is he called to sign? He plus one and he is between Hi. Over too. Two three high. All right too

Numerade Educator

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…

Find parametric equations for the path of a particle that moves along the ci…

Find parametric equations for the path of a particle thatmoves along the…

Find parametric equations and a parameter interval for the motion of a parti…

Find parametric equations and a parameter interval for the motionof a pa…

Circles Find parametrizations to model the motion of a particle that starts …

Find parametric equations for an object that moves along the ellipse $\frac{…

Consider the following parametric equations.a. Eliminate the parameter t…

Parametric Equations for Curves Find parametric equations for the curve with…