The Polar Coordinate System

The pole O, polar axis OA, and a point P(r, θ)

In the polar coordinate system, the fixed point O is called the ______ (or origin).

The pole O, polar axis OA, and a point P(r, θ)

In the polar coordinate system, the fixed point O is called the ______ (or origin).

The fixed ray in the polar coordinate system, usually drawn horizontally to the right from the pole, is called the polar axis or polar ______.

The fixed ray in the polar coordinate system, usually drawn horizontally to the right from the pole, is called the polar axis or polar ______.

In polar coordinates (r, θ), the directed angle θ is measured positive when rotated in which direction?

How many different sets of polar coordinates can represent the same point?

If r is negative in the polar coordinates (r, θ), the point lies:

Relating (x, y) and (r, θ)

The relation between Cartesian coordinates (x, y) and polar coordinates (r, θ) includes x = r cosθ and y =

From \(x = r\cos\theta\) and \(y = r\sin\theta\), and using \(\cos^2\theta + \sin^2\theta = 1\), express \(r^2\) in terms of x and y.

From \(x = r\cos\theta\) and \(y = r\sin\theta\), and using \(\cos^2\theta + \sin^2\theta = 1\), express \(r^2\) in terms of x and y.

From \(x = r\cos\theta\) and \(y = r\sin\theta\) (with \(x \neq 0\)), what is \(\tan\theta\) equal to?

Which of the following polar coordinate pairs all represent the same point as \((4,\ \tfrac{5}{6}\pi)\)?

If a curve in a plane is expressed in polar coordinates as \(r = f(\theta)\), then along the curve: