Chapter 9, Part 2 Formulas Flashcards
0
Q
θ with -θ and r with -r
A
about θ=π/2 (y-axis)
1
Q
θ with -θ
A
about the polar axis (x-axis)
2
Q
θ with π-θ
A
about θ=π/2 (y-axis)
3
Q
r with -r
A
about the pole (origin)
4
Q
θ with π+θ
A
about the pole (origin)
5
Q
r=sin(aθ) or r=cos(aθ)
A
flower–if a is odd, there are a petals, and if a is even, there are 2a petals.
6
Q
r=a+asinθ
r=a-asinθ
r=a+acosθ
r=a-acosθ
A
cardioid
7
Q
r=a+bsinθ
r=a-bsinθ
r=a+bcosθ
r=a-bcosθ
A
Limaςon (with a loop if b>a)
8
Q
r^2=asin(bθ)
r^2=acos(bθ)
A
Lemniscate (think infinity)
9
Q
sin(x+y)
A
sin(x)cos(y)+cos(x)sin(y)
10
Q
sin(x-y)
A
sin(x)cos(y)-cos(x)sin(y)
11
Q
cos(x+y)
A
cos(x)cos(y)-sin(x)sin(y)
12
Q
cos(x-y)
A
cos(x)cos(y)+sin(x)sin(y)
13
Q
tan(x+y)
A
(tan(x)+tan(y))/(1-tan(x)tan(y))
14
Q
tan(x-y)
A
(tan(x)-tan(y))/(1-tan(x)tan(y))
