Unit 4 Flashcards
A vector is perpendicular/orthogonal if…
the dot product = 0
A vector is parallel if…
a1/a2 = b1/b2
What is the formula for rectangular coordinates to polar?
X = r * cos theta Y = r * sin theta
Modulus, magnitude, hypotenuse, radius
All the same. ||V||
What is the formula for polar coordinates to rectangular?
R = root(x^2+y^2) Theta = arctan (y/x)
What is the interval when in polar coordinates?
between 0 and 2pi, must also be in the same quadrant.
What are complex numbers in rectangular form?
a+bi
What are complex numbers in polar form?
r(cos theta + i sin theta)
What is the formula for magnitude of a vector?
root(a^2+b^2)
What is the formula for a unit vector?
(1/||v||)*<a,b>
When finding the nth root, what is K?
K is n-1
When finding the nth root, what is N?
N is the root number
What is the formula for finding the nth root?
Zk = ^n root(r)[cos (theta+2piK)/n + i sin (theta+2piK)/n]
What is DeMoivre’s theorem formula?
(a+bi)^2 = r^n[cos (thetan)+isin (thetan)]
What is the formula for finding the angle between two vectors?
arccos ([vw]/||v||||w||) = theta
What is the formula for a vector V projected onto W?
ProjwV = ([vw]/||w||^2)w
What is the formula for finding work done?
W = F * D
When finding work formula, what is F?
F is a force vector
What is F denoted by in a work calculation?
force number*(cos theta)i+forcenumber(sin theta)j
When finding work formula, what is D?
D is a distance vector
What is D denoted by in a work calculation?
<x2-x1,y2-y1>
What is a parametric equation?
An equation that models the travel of an object or projectile
What is the formula for X in a parametric equation?
X = Vo (cos theta)t + Xo
What is the formula for Y in a parametric equation?
Y = -1/2 * gt^2+(VoSin theta)*t + Yo
