Coordinates in 3-D, Polar Coordinates, Precalculus
posted by Cambridge .
Let a and b be real numbers. Describe the graph of r = a cos (theta + b) as much as possible. (The intent of this question is to get as specific a description as possible that holds for all possible values of a and b.)
How would I proceed on this problem? I know r = cos theta is a plot of a circle
but how would I insert a and b in there? Thanks
Have some fun here, changing the values of a and b
I used a=4 and b=3
Notice I also placed a domain on Ø from -2π to +2π
things really get interesting if you put a coefficient in front of the Ø , such as
r = 4cos(7Ø + 3)
cos(θ+b) just rotates the figure around the origin by b.
In effect, it rotates the x- and y-axes by b.
acos(θ+b) scales the rotated figure by a factor of a.