Unit 3 Exam

cartesian to polar

x = rcosθ

y = rsinθ

x² + y² = r²

tanθ = y/x

trig identities

sin²x = (1-cos(2x))/2

cos²x = (1+cos(2x))/2

sin²x + cos²x = 1

polar area formula

½ ∫ r² dθ

½ ∫ r(big)² - r(small)² dθ

solve differential equation

find function that satisfies differential equation

separation of variables

dy/dt = ky

y = Ce^(kt)

equilibrium solution

a constant solution to a differential equation where the derivative is zero

to see if a function is a solution to a differential equation

1. take derivative of potential solution

2. plug in potential solution for y into derivative

3. see if they match- if they do, then solution works