Question

The graph of a limacon curve is given. Without using your graphing calculator, determine which equation is correct for the graph. [-5, 5] by [-5, 5]

a. r = 2 - 2 sin θ
b. r = 3 - 2 sin θ
c. r = 2 + 2 sin θ
d. r = 1 - 3 sin θ

Answer 1

b

Explanation:

Answer 2

A

Explanation:

A limacon curve passes trough the point
`\left((\pi)/(2),0\right)`, this means when
`\theta =(\pi)/(2),` the distance
`r=0.`

Note that

`\sin (\pi)/(2) =1,`

so, if
`r=a+b\sin \theta,`

then

`r\left((\pi)/(2)\right)=a+b=0\\ \\a=-b`

The only option which shows a = -b is option A.