Question

Summarize the family of graphs, r = a, r = (a)cos(theta), and r = (a)sin(theta), so that you can graph them without a graphing utility.

Answer 1

\(r=a\) means the radius is \(a\) i.e. it is a circle with center \((0,0)\) and radius \(a\)

Answer 2

btw it is always \[r^2=x^2+y^2\] so \[r=a\] means \[x^2+y^2=a^2\]

Answer 3

do you know what \[r=\sin(\theta)\] looks like?

Answer 4

Yes a circle with positive y and a diameter of 1.

Answer 5

yes so \[r=a\sin(\theta)\]has diameter \(a\)

Answer 6

sits above the x axis if \(a>0\) below if \(a<0\)

Answer 7

Ah right. and I assume \[r = a \cos( \theta)\] is a circle that has all x points to the right of the origin.

Answer 8

yes unless \(a<0\)in which case it is always on the other side