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Identify Special Polar Graphs: Lemniscates

Which one of the following equations represents a lemniscate?

$r=a+b\ \cos\ \cos\alpha$

$r^2=a^2\alpha$

$r=\cos\cos3\alpha$

Which one of the following formulas that generate the graph of a lemniscates ?

r=acos $\alpha$

r=cos $\alpha$

$r^2=a^2\cos2\alpha$

What does following figure represents?

Circle

limacon

lemniscate

Complete :
A lemniscate containing the sine function will be symmetric to the ________

pole

polar axis

line $\alpha$ = π/2

Which one of the following formulas that generate the graph of a lemniscates ?

r=acos $\alpha$

r=a sin $\alpha$

$r^2=a^2\sin2\alpha$

Is the sentence true of false?
The figure represents the graph of $r^2=2\alpha$

True

False

Is the sentence true of false?
The lemniscate is a polar curve resembling the infinity symbol ∞

True

False

Is the sentence true of false?
The figure represents the graph of $r^2=\cos\cos2\alpha$

True

False

Is the sentence true of false?
The figure represents the graph of r²= 2 $\alpha$

True

False

Complete :
A lemniscate containing the cosine function will be symmetric to________

pole

polar axis

line $\alpha$ = π/2

Questions

Time

Score

Identify Special Polar Graphs: Lemniscates

Which one of the following equations represents a lemniscate?

﻿r=a+b cos⁡ cos⁡αr=a+b\ \cos\ \cos\alphar=a+b cos cosα﻿

﻿r2=a2αr^2=a^2\alphar2=a2α﻿

﻿r=cos⁡cos⁡3αr=\cos\cos3\alphar=coscos3α﻿

Which one of the following formulas that generate the graph of a lemniscates ?

r=acos﻿α\alphaα﻿

r=cos﻿α\alphaα﻿

﻿r2=a2cos⁡2αr^2=a^2\cos2\alphar2=a2cos2α﻿

What does following figure represents?﻿

Circle

limacon

lemniscate

Complete :A lemniscate containing the sine function will be symmetric to the ________

pole

polar axis

line ﻿α\alphaα﻿ = π/2

Which one of the following formulas that generate the graph of a lemniscates ?

r=acos﻿α\alphaα﻿

r=a sin﻿α\alphaα﻿

﻿r2=a2sin⁡2αr^2=a^2\sin2\alphar2=a2sin2α﻿

Is the sentence true of false?The figure represents the graph of ﻿r2=2αr^2=2\alphar2=2α﻿

True

False

Is the sentence true of false?The lemniscate is a polar curve resembling the infinity symbol ∞

True

False

Is the sentence true of false?The figure represents the graph of ﻿r2=cos⁡cos⁡2αr^2=\cos\cos2\alphar2=coscos2α﻿

True

False

Is the sentence true of false?The figure represents the graph of r2= 2﻿α\alphaα﻿

True

False

Complete :A lemniscate containing the cosine function will be symmetric to________

pole

polar axis

line ﻿α\alphaα﻿ = π/2

Incorrect

Great!

$r=a+b\ \cos\ \cos\alpha$

$r^2=a^2\alpha$

$r=\cos\cos3\alpha$

r=acos $\alpha$

r=cos $\alpha$

$r^2=a^2\cos2\alpha$

What does following figure represents?

Complete :
A lemniscate containing the sine function will be symmetric to the ________

line $\alpha$ = π/2

r=acos $\alpha$

r=a sin $\alpha$

$r^2=a^2\sin2\alpha$

Is the sentence true of false?
The figure represents the graph of $r^2=2\alpha$

Is the sentence true of false?
The lemniscate is a polar curve resembling the infinity symbol ∞

Is the sentence true of false?
The figure represents the graph of $r^2=\cos\cos2\alpha$

Is the sentence true of false?
The figure represents the graph of r²= 2 $\alpha$

Complete :
A lemniscate containing the cosine function will be symmetric to________

line $\alpha$ = π/2