Parametric and Polar

rate of change with respect to x or y

dx/dt or dy/dt

slope of line tangent

dy/dx

find dy/dtheta given r(theta)

y = rsintheta, product rule, plug in

find dx/dtheta given r(theta)

x=rcostheta, product rule, plug in

distance

integral of distance formula, sqrt((dy/dt)² + (dx/dt)²)

speed

plug in t value in distance formula

Quadrant 2 Reference Angle

pi minus

Quadrant 3 Reference Angle

pi plus

Quadrant 4 Reference Angle

2pi minus

greatest distance from origin to point on a polar curve

r’(theta) = 0, then plug in each theta value for r(theta), greatest abs value = farthest point

write the equation for the tangent line given polar form

y - y(t) = dy/dx (x- x(t)) find x and y with rcostheta rsintheta

length of curve

integral from a to b sqrt(r² + (dr/dtheta)²)

farthest to left/right

dx/dt = 0, find t, test max/min

evaluate the integral with the i and j thing

evaluate each seperately, <first, second>

initial value problem with the i and j thing, r(0) = j

j = 0i + 1j, integrate seperately to get x and y, set equal to 0 and 1, solve for c

area common to two curves

find intersection angles, determine which is smaller where (0 to angle, angle to quadrantal), plug the smaller one into ½ integral of r²