Refer a friend and earn $50 when they subscribe to an annual planRefer Now

Get the answer to your homework problem.

Try Numerade Free for 30 Days

Like

Report

Use the graphs of $ x = f(t) $ and $ y = g(t) $ to sketch the parametric curve $ x = f(t) $, $ y = g(t) $. Indicate with arrows the direction in which the cuve is traced as $ t $ increases.

When $t=-1,(x, y)=(1,1) .$ As $t$ increases to $0, x$ and $y$ both decrease to 0As $t$ increases from 0 to $1, x$ increases from 0 to 1 and $y$ decreases from 0 to$-1 .$ As $t$ increases beyond $1, x$ continues to increase and $y$ continues todecrease. For $t<-1, x$ and $y$ are both positive and decreasing. We couldachieve greater accuracy by estimating $x$ - and $y$ -values for selected values of $t$from the given graphs and plotting the corresponding points.

02:30

Bobby B.

Calculus 2 / BC

Chapter 10

Parametric Equations and Polar Coordinates

Section 1

Curves Defined by Parametric Equations

Parametric Equations

Polar Coordinates

Campbell University

Harvey Mudd College

Baylor University

University of Michigan - Ann Arbor

Lectures

01:11

In mathematics, integratio…

06:55

In grammar, determiners ar…

02:29

Use the graphs of $ x = f(…

02:16

03:07

$19-21=$ Use the graphs of…

03:12

02:35

01:17

Sketch the curve with the …

03:23

Use point plotting to grap…

04:21

Sketch the curve by using …

00:55

01:27

So if we want to sketch this graph in the Cartesian plane, let's first go ahead and maybe just graph a couple of these points. That might be easy for us to find Well, over here. Um, so they give us 11 so we can estimate negative one is probably around here. Negative one is here, so let's just make a little chart. So when t is equal to negative one, it looks like First X is equal to one. And why is going to be equal to one also? Okay, um, when tea is able to zero, it looks like ax zero. It also looks like Why is zero And then when t is equal to one X is one again, and then it looks like why is equal to, uh, negative one? So let's come over here now and just graph those points that we have X Y, uh, I'll just put all those are just gonna be one for the tick marks. So at negative one, we have X is equal to one. Why is it good to one? So that would be right here, and this is T is equal to negative one. Now, when t 00 both X and wire zero. Alright. T is zero. And then when t is he going to one Access one again and then y is negative one. So this is t is he took one. Now we can kind of see So X is going to grow a lot quicker than why it's so when we're going through this or actually I should say access first, going to be decreasing to the left and why is always going to be decreasing So we should know that why should always be going down and then X was going to decrease up until we hit zero and they will start increasing again. So that means we can just go ahead and connect these points and it will kind of look like this quadratic here now for us to figure out what the direction is, we're just going to follow the points. So it goes from negative 1 to 0 and then 0 to 1. So this here is going to be a sketch of what this would look like in the XY plane

View More Answers From This Book

Find Another Textbook

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…

Use the graphs of $ x = f(t) $ and $ y = g(t) $ to sketch the parametric cur…

$19-21=$ Use the graphs of $x=f(t)$ and $y=g(t)$ to sketch theparametric…

Sketch the curve with the given vector equation. Indicate with an arrow the …

Use point plotting to graph the plane curve described by the given parametri…

Sketch the curve by using the parametric equations to plot points. Indicate …

04:05

Use series to approximate the definite integral to within the indicated accu…

01:04

Use a Maclaurin series in Table 1 to obtain the Maclaurin series for the giv…

02:42

A stone is dropped from the upper observation deck (the Space Deck) of the C…

01:38

Graph the curve with parametric equations$$ x = (1 + \cos 16t) \cos t $$…

00:58

Prove that the series obtained in Exercise 13 represents $ \cos x $ for all …

Use a computer to graph the curve with the given vector equation. Make sure …

01:49

04:12

(a) Show that $ \frac{dB}{ds} $ is perpendicular to $ B $.(b) Show that …

02:10

Use the binomial series to expand the function as a power series. State the …

03:21

92% of Numerade students report better grades.

Try Numerade Free for 30 Days. You can cancel at any time.

Annual

0.00/mo 0.00/mo

Billed annually at 0.00/yr after free trial

Monthly

0.00/mo

Billed monthly at 0.00/mo after free trial

Earn better grades with our study tools:

Textbooks

Video lessons matched directly to the problems in your textbooks.

Ask a Question

Can't find a question? Ask our 30,000+ educators for help.

Courses

Watch full-length courses, covering key principles and concepts.

AI Tutor

Receive weekly guidance from the world’s first A.I. Tutor, Ace.

30 day free trial, then pay 0.00/month

30 day free trial, then pay 0.00/year

You can cancel anytime

OR PAY WITH

Your subscription has started!

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".

Receive weekly guidance from the world's first A.I. Tutor, Ace.

Mount Everest weighs an estimated 357 trillion pounds

Snapshot a problem with the Numerade app, and we'll give you the video solution.

A cheetah can run up to 76 miles per hour, and can go from 0 to 60 miles per hour in less than three seconds.

Back in a jiffy? You'd better be fast! A "jiffy" is an actual length of time, equal to about 1/100th of a second.