What is Cartesian and polar form?

Polar Coordinates. Main Concept. The Cartesian coordinate system is a two-dimensional coordinate system using a rectilinear grid: • The x and y coordinates of a point measure the respective distances from the point to a pair of perpendicular lines in the plane called the coordinate axes, which meet at the origin.

What is path coordinate?

The curve in space described by the particle is called the path, or trajectory. We introduce the path or arc length coordinate, s, which measures the distance traveled by the particle along the curved path.

What is polar form?

The polar form of a complex number is another way to represent a complex number. The form z=a+bi is called the rectangular coordinate form of a complex number. The horizontal axis is the real axis and the vertical axis is the imaginary axis.

What are polar measurements?

A system of coordinates in which the location of a point is determined by its distance from a fixed point at the center of the coordinate space (called the pole) and by the measurement of the angle formed by a fixed line (the polar axis, corresponding to the x-axis in Cartesian coordinates) and a line from the pole …

What are normal and tangential coordinates?

The normal-tangential coordinate system centers on the body in motion. In the normal-tangential coordinate system the particle itself serves as the origin point. The t-direction is the current direction of travel and the n-direction is always 90 degrees counter-clockwise from the t-direction.

What is amplitude of Z?

The polar representation of z is z = r(cos θ + i sin θ). Here, r is the modulus of z and θ is called the amplitude or argument of the complex number. The formula to find the amplitude of a complex number is: θ = tan-1(y/x) This value is defined by the function 2nπ + θ, where n ∈ I (i.e., the set of all integers).

How do you find the polar coordinates?

Locate the angle on the polar coordinate plane. Refer to the figure to find the angle: 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. Plot the given point.

How do you convert rectangular coordinates to polar coordinates?

To convert from polar to rectangular coordinates, use the trigonometric ratios and where r is the hypotenuse of the right triangle. The rectangular form of the polar coordinate (r, θ) is (rcos θ, rsin θ). To convert from rectangular to polar coordinates, use the Pythagorean Theorem and the trigonometric ratio.

What is a polar coordinate system?

In mathematics, the polar coordinate system is a two-dimensional coordinate system in which each point on a plane is determined by a distance from a reference point and an angle from a reference direction.

How to convert rectangular to polar?

To convert from rectangular to polar: r2 = x2 +y2 tanθ = y x This is where these equations come from: