Parametric and polar

Question 1

dy / dx

Answer 1

[dy/dt] / [dx/dt]

Question 2

d^2y / dx^2

Answer 2

(d/dt) * [dy/dx]) / (dx/dt)

Question 3

Speed formula

Answer 3

sqrt [ (dx/dt)^2 + (dy/dt)^2 ] dt

Question 4

Total distance formula

Answer 4

∫ba sqrt [ (dx/dt)^2 + (dy/dt)^2 ] dt

Question 5

Equation to find r

Answer 5

r^2 = sqrt (x^2 + y^2)

Question 6

Equation to find θ

Answer 6

tan(θ) = y / x

Question 7

Equation to find x

Answer 7

x = r cos (θ)

Question 8

Equation to find y

Answer 8

y = r sin (θ)

Question 9

dy / dx (polar)

Answer 9

dy/dx = [ (d/dθ) * (r cos(θ)) ] / [ (d/dθ) * (r sin(θ)) ]

Question 10

Area formula (polar)

Answer 10

∫ba 1/2 *(r(θ))^2 dθ