Coordinates in 3D, 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
http://www.wolframalpha.com/input/?i=plot+r+%3D4cos%28Ø%2B3%29+%2C6.28+%3C+Ø+%3C+6.28
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 yaxes by b.
acos(θ+b) scales the rotated figure by a factor of a.
Respond to this Question
Similar Questions

Polar to Rectangular Form
The letters r and theta represent polar coordinates. Write each equation in rectangular coordinates (x, y) form. Let t = theta (1) r = sin(t) + 1 (2) r = sin(t)  cos(t) 
Math (Calculus)
Given any Cartesian coordinates, (x,y), there are polar coordinates (r,theta) with –pi/2< theta < pi/2. Find polar coordinates with –pi/2 < theta < pi/2 for the following Cartesian coordinate: If (x,y) = (11,–7) then … 
Math ! Please Help !
1.Graph the polar equation r=32sin(theta) 2. Find the polar coordinates of 6 radical 3,6 for r > 0. 3. Find the rectangular coordinates of (7, 30°). 4. Write the rectangular equation in polar form. (x – 4)2 + y2 = 16 5. Write … 
Calculus please help !
1.Graph the polar equation r=32sin(theta) 2. Find the polar coordinates of 6 radical 3,6 for r > 0. 3. Find the rectangular coordinates of (7, 30°). 4. Write the rectangular equation in polar form. (x – 4)2 + y2 = 16 5. Write … 
Precalculus; urgent ! Please help !
1.Graph the polar equation r=32sin(theta) 2. Find the polar coordinates of 6 radical 3,6 for r > 0. 3. Find the rectangular coordinates of (7, 30°). 4. Write the rectangular equation in polar form. (x – 4)2 + y2 = 16 5. Write … 
Math Graph
In polar coordinates, the graph r=sin(θ)/cos^2(θ) represents the function y=(a_n)*x^n+(a_(n−1))*x^(n−1)+…+a_0 in Cartesian coordinates, where n is a positive integer and (a_i) are real numbers. What is the value … 
Precalc  Coordinates in 3D  Polar Coords
Show that r = cos theta is a graph of a circle with diameter 1 from 0,0 to 0,1 How to do this algebraically? 
Precalculus
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. For example, if … 
Calculus (polar coordinates)
Use polar coordinates to set up the double integral x dA, where the bounds are given by the region lying in the intersection of the 2 circles r = 2 sin (theta) and r = 2 cos theta. Thanks for any help! 
Polar, Cylindrical, and Spherical Coordinates
Let C be a circle that passes through the origin. Show that we can find real numbers s and t such that C is the graph of r = 2s*cos(theta + t) I think that I could start by writing it like R^2=(xh)^2+(yk)^2 where R is the radius …