What does it mean when r is negative in polar coordinates?

From this sketch we can see that if r is positive the point will be in the same quadrant as θ . On the other hand if r is negative the point will end up in the quadrant exactly opposite θ . In polar coordinates there is literally an infinite number of coordinates for a given point.

Where is r negative polar coordinates?

The directed distance, r, is measured from the pole to point P. If point P is on the terminal side of angle θ, then the value of r is positive. If point P is on the opposite side of the pole, then the value of r is negative.

What is r Theta in polar coordinates?

The Greek letter θ (theta) is often used to denote an angle, and a polar coordinate is conventionally referred to as (r, θ) instead of (x, y). Thus, when dealing with polar coordinates, we’ll now use “theta” as the preferred variable name for the angle. They each take one argument, an angle measured in degrees.

Can Theta be negative in polar coordinates?

Recall that a positive value of θ means that we are moving counterclock- wise. But θ can also be negative. A negative value of θ means that the polar axis is rotated clockwise to intersect with P. Thus, the same point can have several polar coordinates.

Is R always positive in polar form?

In the polar coordinate system, the ordered pair will now be (r, θ). The ordered pair specifies a point’s location based on the value of r and the angle, θ, from the polar axis. The value of r can be positive, negative, or zero.

Why is r sin theta circle?

First, the length is given by sin (theta), so we expect it to trace out a circle at the origin since it goes from 0 to 1 and back to 0. Then as theta goes from Pi to 2Pi, the value of r is negative, but the angle is in the third and fourth quadrant, so it will trace the same circle again.

How do you graph negative R in polar coordinates?

Explain how polar coordinates are graphed. Determineθ θ for the point, then mover r units from the pole to plot the point. Ifr r is negative, mover r units from the pole in the opposite direction but along the same angle. The point is a distance ofr r away from the origin at an angle ofθ θ from the polar axis.