How to find the points, in both polar coordinates and rectangular coordinates corresponding to the values.

Question

$r=1+3sin(t)$

where $t=0,\pi/6, \pi/4,\pi/3,\pi/2,3\pi/4,\pi,3\pi/2,2\pi$

How to find the points, in both polar coordinates and rectangular coordinates corresponding to the values.

Can anyone show how to do this

Answer 1

For polar coordinates $(r,t)$ simply note that

• $t=0 \implies r =1$
• $t=\pi/6 \implies r =1+3/2$
• ...

and so on.

For cartesian coordinates $(x,y)$ let use

• $x=r\cos t$
• $y= r \sin t$