Chapter 9 Flashcards
R cos theta = c
Vertical line
R sin theta = c
Horizontal line
Theta = alpha … alpha = a value for the angle
Straight line going through origin at angle alpha
x^2 + y^2 = c^2, c > 0
Circle
Center at pole
Radius = c
r = c, c > 0
Circle
Center at pole
Radius = c
x^2 + y^2 = ± 2cx, c > 0
Circle
Radius = c
Center on polar axis (x) at either (c, 0) or (-c, 0)
x^2 + y^2 = ± 2cy, c > 0
Circle
Radius = c
Center on pi/2 axis at either (pi/2, c) or (pi/2, -c)
r = ± 2c cos theta, c > 0
Circle
Radius = c
Center on polar axis (x) at either (c, 0) or (-c, 0Circle
Radius = c
Center on polar axis (x) at either (c, 0) or (-c, 0)
r = ± 2c sin theta, c > 0
Circle
Radius = c
Center on pi/2 axis at either (pi/2, c) or (pi/2, -c)
r = c ± c cos theta, c > 0
Cardioid
Polar intercept: (2c, 0) or (-2c, 0)
Symmetry: Polar
r = c ± c sin theta, c > 0
Cardioid
Polar intercept: (0, 2c) or (0, -2c), & (0,0)
Symmetry: pi/2 axis
r = c ± b cos theta, 0 < b < c
Limacon w/o inner loop
Axis: Polar
[a+b], 0) or (-[a+b], 0
([a-b], 0) or (-[a-b], 0)
r = c ± b sin theta, 0 < b < c
Limacon w/o inner loop
Axis: pi/2
b-a, 0), (b+A, 0
r = c ± b cos theta, 0 < c < b
Limacon w/ inner loop
Polar
Loop goes from (0,0) to (b-a, 0) or (a+b, 0)
r = c ± b sin theta, 0 < c < b
Limacon w/ inner loop
Loop goes from (0,0) to (b-a, 0) or (a+b, 0)
