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Coordinates in 3-D, Polar Coordinates, Precalculus

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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.

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