Final Chapters Flashcards
Rectangular to polar
Find theta
Tan^-1(y/X) if X>0
Tan^-1(y/X) + pie if X 0
3pie/2 if X=0 and y
Polar to rectangular
X=rcos
Y=rsin
R=2asin
R=-2asin
R=2acos
R=-2acos
Radius a for all
Center (0,a)
Center (0,-a)
Center (a,0)
Center (-a,0)
Symmetric with X axis
Replace theta with - theta
If same equation then it is symmetric
Symmetric with y axis
Replace theta with pie-theta
If same equation. Then is symmetric
Symmetric with pole/origin
Replace r by -r
If same equation then is symmetric
Cardioid with inner loop equations
R=a(1+cos)
R=a(1-cos)
R=a(1+sin)
R=a(1-sin)
Limacons w/inner loop
R=a+bcos
R=a-bcos
R=a+Bsin
R=a-Bsin
Where a>0 . b>0 . a>b
Limacons with inner loop
R=a+bcos
R=a-bcos
R=a+bsin
R=a-bsin
A>0. B>0. A
Rose
R=acos(N theta)
R=asin(N theta)
If n is even then double amount of petal is n
If n is odd then n number of petals.
a+bi
a-bi(a+bi)
i^2
-1
Norm of Z
Square root of (z)(complex conjugation of z)
X+iy
Rcos+irsin
Z1(Z2)
r1r2(cos(theta1+theta2) + isin(theta1+theta2))
Z1/Z2
r1/r2(cos(theta1-theta2) +isin(theta1-theta2))
Vector from one to another
Head -tail
P1 tail
P2 head
Adding vectors
V+w
<a> </a>
Subtracting vectors
V-W
V+ (-1)W
Magnitude
||V||
Square root of a squared +b squared
Dot product
V•W
ac+bd
Finding theta
Cos(theta) = V•W / (||V||•||W||)
Magnitude
||V||^2=a^2+b^2=V•V
Parellel
Lie on same line
If
V=aW for some a number
Orthangonal
Right angle
If V•W=0
Projection of V1
V1=V•W / W•W (W)
Projection V2
V-V1
Work
F•PQ
Rectangular to polar
To find r
Square root X squared plus y squared
