What do negative polar coordinates mean?

What do negative polar coordinates mean?

When the radius is negative: When graphing a polar coordinate with a negative radius, you move from the pole in the direction opposite the given positive angle (on the same line as the given angle but in the direction opposite to the angle from the pole).

Can a polar coordinates be negative?

Polar coordinates are usually defined such that every point (x,y) in R2 can be reassigned some value r≥0 and 0≤θ<2π. In this formulation, r is a distance. It cannot be negative.

What is Y in polar?

Summary: to convert from Polar Coordinates (r,θ) to Cartesian Coordinates (x,y) : x = r × cos( θ ) y = r × sin( θ )

What happens if r is negative 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.

How do you know if polar coordinates are positive or negative?

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. The polar coordinates of a point can be written as an ordered pair ( r, θ).

What happens if r is negative in 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.

When to graph Polar coordinates with negative values?

Sometimes your geometry teacher may spice things up a bit with complicated polar coordinates — points with negative angles and/or radii. The following list shows you how to plot in three situations — when the angle is negative, when the radius is negative, and when both are negative.

When to use a negative R R in a coordinate pair?

The last two coordinate pairs use the fact that if we end up in the opposite quadrant from the point we can use a negative r r to get back to the point and of course there is both a counter clock-wise and a clock-wise rotation to get to the angle.

How to show negative radius points in a?

Double click on the polar plot, select the layer branch for the polar plot on the left panel of the Plot Details dialog. Click on the Display tab, make sure to select the Show Negative Radius Points in Opposite Quadrant check box in the Polar Plots group. Click OK to close the Plot Details dialog.

How to identify polar coordinates in calculus 2?

To identify it let’s take the Cartesian coordinate equation and do a little rearranging. Now, complete the square on the x x portion of the equation. So, this was a circle of radius 4 and center (−4,0) ( − 4, 0).