Page 52 - Calculus for the Clueless

If you look at the picture of the cycloid, the second derivative shows the curve is always down, since the second
derivative is always negative a is positive, except at multiples of 2π, where the curve comes to a point. The
parameter is extremely useful here, as it always is when it is used.

Polar Coordinates

In the past, you should have had a teeny, tiny bit of experience with polar coordinates, namely how to graph a
point, say (4, π/6). The following is a summary of all the things you should know on this topic.

Rule 1

Relationship between (x, y) and (r, θ):

A. r = [x + y )
2
2 1/2
B. θ = angle measured from positive x-axis, positive in a counterclockwise direction

C. x = r cos θ

D. y = r sin θ

Rule 2

Every point has an infinite number of representations.

n integer

Rule 3

A. r = a is a circle center at the origin, radius a.

B. θ = c is a line through the origin.