polar graphing

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Last updated 8:16 PM on 4/5/26
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12 Terms

1
New cards

both r=acosθ and r=asinθ

  • circle

  • passes through the origin

  • diameter = a

2
New cards

r=acosθ

  • x axis symmetry

  • a > 0 → center is (a/2,0); x int is (a,0)

  • a < 0 → center is (-a/2,0); x int is (-a,0)

3
New cards

r=asinθ

  • y axis symmetry

  • a > 0 → center is (0,a/2); y int is (0,a)

  • a < 0 → center is (0,-a.2); y int is (0,-a)

4
New cards

both r=acosnθ and r=asinnθ

  • length of petals = a

  • n = even → 2n petals

  • n = odd → n petals

  • petals are evenly spaced

  • period = 2pi/n

5
New cards

r=acosnθ

  • x axis symmetry

  • if a > 0, petal on positive x axis (a, 0)

  • if a < 0, petal on negative x axis (a, pi)

6
New cards

r=asinnθ

  • y axis symmettry

  • if a > 0, petal on pi/2n (a, pi/2n)

  • if a < 0, petal on -pi/2n (a, -pi/2n)

7
New cards

both r = a+bcosθ and r = a+bsinθ

  • sign of a = no effect

  • ignore signs

  • a < b → loop inside length = b-a

  • a = b → cardioid (heart shape)

  • a > b → becomes more circular— will not pass through the origin

8
New cards

r= a+bcosθ

  • x axis symmetry

  • b > 0 → symmetric on positive x axis

  • b < 0 → symmetric on negative x axis

  • ignore signs

  • one x intercept: b + a units from pole

  • y intercepts are a units away from pole

9
New cards

r= a+bsinθ

  • y axis symmetry

  • if b > 0 → symmetric on positive y axis

  • if b < 0 → symmetric on negative y axis

  • ignore signs

  • one y intercept: b+a units from pole

  • x intercepts are a units away from pole

10
New cards

both r=a+bcosnθ and r=a+bsinnθ

  • ignore signs

  • a < b →

    • n big petals (length = b+a)

    • n little petals (length = b-a)

  • n = odd → little petals inside big petals

  • n = even → little petals between big petals

  • a = b → n petals (length = b+a)

  • a > b → n petals but doesn’t go through pole (length = b+a)

    • shape becomes like a propeller

  • period = 2pi/n

11
New cards

r=a+bcosnθ

  • x axis symmetry

  • a < b

    • if b > 0, big petal on positive x axis

    • if b < 0, little petal on negative x axis

  • a = b or a > b

    • if b > 0 petal on positive x axis

    • if b < 0 and n = odd petal on negative x axis

    • if b > 0 and n = even, no petal on x axis

12
New cards

r=a+bsinnθ

  • θ=pi/2n symmetry

  • a < b or a = b or a > b

    • if b > 0, big petal on pi/2n

    • if b < 0, big petal on -pi/2n