any-methods-to-sketch-these-curves-r-a-1-cos-r-a-b-cos-a-gt-b-r-a-bcos-a-lt-b-

Question Number 86198 by Rio Michael last updated on 27/Mar/20

any methods to sketch these curves r = a(1−cosθ) r= a + b cosθ a>b r= a + bcosθ a<b

$$\mathrm{any}\:\mathrm{methods}\:\mathrm{to}\:\mathrm{sketch}\:\mathrm{these}\:\mathrm{curves} \\ $$$$\:\mathrm{r}\:=\:\mathrm{a}\left(\mathrm{1}−\mathrm{cos}\theta\right) \\ $$$$\:\mathrm{r}=\:\mathrm{a}\:+\:\mathrm{b}\:\mathrm{cos}\theta\:\:{a}>{b} \\ $$$$\:\mathrm{r}=\:\mathrm{a}\:+\:\mathrm{bcos}\theta\:\:\:{a}<{b} \\ $$

Commented by Prithwish Sen 1 last updated on 27/Mar/20

To sketch any graph you have to keep in your mind the following things i) Symmetry : whether the graph is symmetric respect to X ,Y axis or to the line y=x or to the origin. ii)Intercept : the intercept of x and y axes iii)asymptotes: whether the curve has any asymptotes iv)extension or range of the curve v)Any special point Now go and sketch the curve. Good luck

$$\mathrm{To}\:\mathrm{sketch}\:\mathrm{any}\:\mathrm{graph}\:\mathrm{you}\:\mathrm{have}\:\mathrm{to}\:\mathrm{keep}\:\mathrm{in}\:\mathrm{your} \\ $$$$\mathrm{mind}\:\mathrm{the}\:\mathrm{following}\:\mathrm{things} \\ $$$$\left.\boldsymbol{\mathrm{i}}\right)\:\boldsymbol{\mathrm{Symmetry}}\::\:\boldsymbol{\mathrm{whether}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{graph}}\:\boldsymbol{\mathrm{is}}\:\boldsymbol{\mathrm{symmetric}}\: \\ $$$$\boldsymbol{\mathrm{respect}}\:\boldsymbol{\mathrm{to}}\:\boldsymbol{\mathrm{X}}\:,\boldsymbol{\mathrm{Y}}\:\boldsymbol{\mathrm{axis}}\:\boldsymbol{\mathrm{or}}\:\boldsymbol{\mathrm{to}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{line}}\:\boldsymbol{\mathrm{y}}=\boldsymbol{\mathrm{x}}\:\boldsymbol{\mathrm{or}}\:\boldsymbol{\mathrm{to}}\:\boldsymbol{\mathrm{the}}\: \\ $$$$\boldsymbol{\mathrm{origin}}. \\ $$$$\left.\boldsymbol{\mathrm{ii}}\right)\boldsymbol{\mathrm{Intercept}}\::\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{intercept}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{x}}\:\boldsymbol{\mathrm{and}}\:\boldsymbol{\mathrm{y}}\:\boldsymbol{\mathrm{axes}} \\ $$$$\left.\boldsymbol{\mathrm{iii}}\right)\boldsymbol{\mathrm{asymptotes}}:\:\boldsymbol{\mathrm{whether}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{curve}}\:\boldsymbol{\mathrm{has}}\:\boldsymbol{\mathrm{any}}\:\boldsymbol{\mathrm{asymptotes}} \\ $$$$\left.\boldsymbol{\mathrm{iv}}\right)\boldsymbol{\mathrm{extension}}\:\boldsymbol{\mathrm{or}}\:\boldsymbol{\mathrm{range}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{curve}} \\ $$$$\left.\boldsymbol{\mathrm{v}}\right)\boldsymbol{\mathrm{Any}}\:\boldsymbol{\mathrm{special}}\:\boldsymbol{\mathrm{point}} \\ $$$$\boldsymbol{\mathrm{Now}}\:\boldsymbol{\mathrm{go}}\:\boldsymbol{\mathrm{and}}\:\boldsymbol{\mathrm{sketch}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{curve}}.\:\boldsymbol{\mathrm{Good}}\:\boldsymbol{\mathrm{luck}} \\ $$

Commented by Rio Michael last updated on 27/Mar/20