Explanation Given: r = 2 sin θ Calculation: The objective is to convert the given polar form in an equation in rectangular form. Polar coordinates of a given point are in the form of ( r , θ ) where r is the distance of the point from origin and θ is the angle measured from positive x − a x i s to that point. The rectangular coordinates are represented as ( x , y ) where x is the horizontal distance of the point and y is the vertical distance. The relation between the rectangular and polar coordinates is x = r cos θ y = r sin θ Squaring and adding the above equation you get the equation in rectangular form as: x 2 + y 2 = r 2 The relation between rectangular and polar coordinates can be shown on a right angled triangle as: From the relation you have: y = r sin θ y r = sin θ Put this value of sin θ in the given relation r = 2 sin θ ...

3rd Edition

ISBN: 9781464125263

Author: Jon Rogawski, Colin Adams

Publisher: W.H. Freeman & Co

See similar textbooks

Concept explainers

Family of Curves

A family of curves is a group of curves that are each described by a parametrization in which one or more variables are parameters. In general, the parameters have more complexity on the assembly of the curve than an ordinary linear transformation. These…

XZ Plane

In order to understand XZ plane, it's helpful to understand two-dimensional and three-dimensional spaces. To plot a point on a plane, two numbers are needed, and these two numbers in the plane can be represented as an ordered pair (a,b) where a and b are…

Euclidean Geometry

Geometry is the branch of mathematics that deals with flat surfaces like lines, angles, points, two-dimensional figures, etc. In Euclidean geometry, one studies the geometrical shapes that rely on different theorems and axioms. This (pure mathematics) ge…

Lines and Angles

In a two-dimensional plane, a line is simply a figure that joins two points. Usually, lines are used for presenting objects that are straight in shape and have minimal depth or width.

Videos

Question

Chapter 12.3, Problem 13E

To determine

An equation in rectangular coordinates.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 12.3, Problem 12E

Chapter 12.3, Problem 14E

Students have asked these similar questions

Find a parameterization for a circle of radius 4 with center (-4,-6,-3) in a plane parallel to the yz plane. Write your parameterization so the y component includes a positive cosine.

~ exp(10). A 3. Claim number per policy is modelled by Poisson(A) with A sample x of N = 100 policies presents an average = 4 claims per policy. (i) Compute an a priory estimate of numbers of claims per policy. [2 Marks] (ii) Determine the posterior distribution of A. Give your argument. [5 Marks] (iii) Compute an a posteriori estimate of numbers of claims per policy. [3 Marks]

2. The size of a claim is modelled by F(a, λ) with a fixed a a maximum likelihood estimate of A given a sample x with a sample mean x = 11 = 121. Give [5 Marks]

Chapter 12 Solutions

Calculus - Standalone book

Ch. 12.1 - Prob. 1PQ Ch. 12.1 - Prob. 2PQ Ch. 12.1 - Prob. 3PQ Ch. 12.1 - Prob. 4PQ Ch. 12.1 - Prob. 5PQ Ch. 12.1 - Prob. 6PQ Ch. 12.1 - Prob. 7PQ Ch. 12.1 - Prob. 1E Ch. 12.1 - Prob. 2E Ch. 12.1 - Prob. 3E

Knowledge Booster

$Calculus$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

An equation in rectangular coordinates.

Solution Summary: The author explains that the equation in rectangular coordinates is x 2 + (y 1) 2 = 1.

Concept explainers

Videos

An equation in rectangular coordinates.

Want to see the full answer?

Chapter 12 Solutions