What does a polar curve represent?

What does a polar curve represent?

A polar curve is a shape constructed using the polar coordinate system. Polar curves are defined by points that are a variable distance from the origin (the pole) depending on the angle measured off the positive x-axis.

What is the Y axis on a polar graph called?

You find two perpendicular lines called axes. The horizontal axis (or x-axis) and vertical axis (or y-axis) intersect at the origin, the point labeled (0, 0). Points are graphed, in polar coordinates, using the ordered pair (r, θ).

How do you plot a polar curve?

Graph the polar curves. r = 3 + 3 sin θ r=3+3\sin{\theta} r=3+3sinθ is like r = a ± a sin θ r=a\pm{a}\sin{\theta} r=a±asinθ, so it’s a cardioid through the origin. We’ll generate a table of values over the interval 0 ≤ θ ≤ 2 π 0\le\theta\le2\pi 0≤θ≤2π.

How do you rotate a polar curve?

Rotate the polar axis about the pole by an amount |θ| : For θ>0 , rotate counterclockwise (green ray at right). For θ=0 , there is no rotation. For θ<0 , rotate clockwise (blue ray at right). For convenience, call this the rotated ray.

How do you do polar coordinates?

How to: Given polar coordinates, convert to rectangular coordinates.

1. Given the polar coordinate (r,θ), write x=rcosθ and y=rsinθ.
2. Evaluate cosθ and sinθ.
3. Multiply cosθ by r to find the x-coordinate of the rectangular form.
4. Multiply sinθ by r to find the y-coordinate of the rectangular form.

What is the polar equation of a circle?

What is the Polar Equation of a Circle? The polar equation of the circle with the center as the origin is, r = p, where p is the radius of the circle.

How do you draw a polar function?

You start there in the following list:

1. Locate the angle on the polar coordinate plane. Refer to the figure to find the angle:
2. Determine where the radius intersects the angle. Because the radius is 2 (r = 2), you start at the pole and move out 2 spots in the direction of the angle.
3. Plot the given point.

Which is the polar equation of a curve?

For concept in aviation that goes by that name, see Polar curve (aviation). For curves given in polar coordinates, see Polar coordinate system § Polar equation of a curve. The elliptic curve E : 4 Y2 Z = X3 − XZ2 in blue, and its polar curve ( E ) : 4 Y2 = 2.7 X2 − 2 XZ − 0.9Z 2 for the point Q = (0.9, 0) in red.

Which is the higher the polar of a C?

Higher polars. The p-th polar of a C for a natural number p is defined as Δ Q pf(x, y, z) = 0. This is a curve of degree n−p.

When is the polar line of a point is L?

The polar line of a point is L if and only if it contains both P and Q, so the poles of L are exactly the points of intersection of the two first polars. By Bézout’s theorem these curves have ( n −1) 2 points of intersection and these are the poles of L.

When to use homogeneous coordinates for polar curve?

It is used to investigate the relationship between the curve and its dual, for example in the derivation of the Plücker formulas . Let C be defined in homogeneous coordinates by f ( x, y, z ) = 0 where f is a homogeneous polynomial of degree n, and let the homogeneous coordinates of Q be ( a , b , c ).