Coordinates in 3-D, Polar Coordinates, Precalculus

posted by .

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

  • Coordinates in 3-D, Polar Coordinates, Precalculus -

    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+%2C-6.28+%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)

  • Coordinates in 3-D, Polar Coordinates, Precalculus -

    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.

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. 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)
  2. 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 …
  3. Math ! Please Help !

    1.Graph the polar equation r=3-2sin(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 …
  4. Calculus please help !

    1.Graph the polar equation r=3-2sin(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 …
  5. Pre-calculus; urgent ! Please help !

    1.Graph the polar equation r=3-2sin(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 …
  6. 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 …
  7. 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?
  8. 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 …
  9. 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!
  10. 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=(x-h)^2+(y-k)^2 where R is the radius …

More Similar Questions