Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 10 - Parametric Equations and Polar Coordinates - Review - Concept Check - Page 729: 4

Answer

(a) Polar coordinates are defined as $(r,θ)$ where $r$ is the length between point $(0,0)$ to the point $(x,y)$ and $θ$ is the angle between $r$ and the $x$ axis. (b) Cartesian coordinates $(x,y)$ of a point in terms of the polar coordinates can be deifned by equations such as $$x=r cos(θ), y=rsin(θ)$$ (c) To find the polar coordinates $(r,θ)$ of a point, we have to first need to calculate the length of the radius $r$, in order to find this we will use the equation $$r=\sqrt (x^{2}+y^{2})$$, Then we need to find the angle between the radius and the x axis, in order to find this we will take the help of the equations $$θ=tan^{-1}\frac{y}{x}$$.

Work Step by Step

(a) Polar coordinates are defined as $(r,θ)$ where $r$ is the length between point $(0,0)$ to the point $(x,y)$ and $θ$ is the angle between $r$ and the $x$ axis. (b) Cartesian coordinates $(x,y)$ of a point in terms of the polar coordinates can be deifned by equations such as $$x=r cos(θ), y=rsin(θ)$$ (c) To find the polar coordinates $(r,θ)$ of a point, we have to first need to calculate the length of the radius $r$, in order to find this we will use the equation $$r=\sqrt (x^{2}+y^{2})$$, Then we need to find the angle between the radius and the x axis, in order to find this we will take the help of the equations $$θ=tan^{-1}\frac{y}{x}$$.
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