parametric to cartesian equation calculator

PARAMETRIC TO CARTESIAN EQUATION CALCULATOR SERIES

If a = b then we have a cycloid as shown above. Related to the cycloid are the curtate cycloid and the prolate cycloid. The following cycloid is the graph created with a circle of radius 1 rolling along the x-axis. The cycloid is the path created when a given point along the circumference of a circle rolls along a line. It was very easy to select the vertices of the triangles (2, 4), (1, 2), and (5, 3).Īlthough parametric equations can be used to graph circles and lines or segements, their real advantage comes when graphing relationships which are neither functions in rectangular nor polar coordinates. The following equations were used to graph a triangle as shown. We can also calculate the slope and length of our segment. For a true line, While this is impossible to actually graph, we can choose the domain of t such that our line extends the length of our screen.

If we want to change the length of our segment, we can change the domain of t. If we vary t from 0 to 1, our segment will start at (a, b) and end at (c, d). Let us assume we want to draw a segment from (a, b) to (c, d). Parametric functions also give us a means of graphing lines and line segments. We will examine the same function, this time only considering the launch angle of. We can see both the maximum height that the projectile reaches and its range from this graph.Ī more interesting use of these parametric equations is to actually watch the trajectory as a function of time. The graph below shows the trajectories taken by an object with an inital velocity of 10 m/s and various launch angles. If we are given the magnitude and angle of the initial velocity, we can calculate the ( x, y) coordinates as a function of time. Consider the following equations for projectile motion. Graphing Calculator 4.0 shows parametric equations in a vector format and Desmos has users put the parameters directly into the coordinate pairs as shown below.Ī traditional use of parametric equations is in physics, particulary when we wish to view two dimensional motion as a function of time. The following graph is from a TI- nspire calculator.Ĭomputer based graphing programs have different methods of showing parametric equations. On handheld graphing calculators, parametric equations are usually entered as as a pair of equations in x and y as written above. To draw a complete circle, we can use the following set of parametric equations. In parametric equations, we have separate equations for x and y and we also have to consider the domain of our parameter. In Cartesian coordinates, we write the equation as

The first set of parametric equations we will consider will be the equation of a circle.

PARAMETRIC TO CARTESIAN EQUATION CALCULATOR SERIES

Any equation that can be written in Cartesian or polar coordinates can also be written as a series of parametric equations, with the advantage of being able to view this relationship as it varies in time. The parameter, t, is often considered as time in the equation. For this exploration, we will be primarily considering equations of x and y as functions of a single parameter, t.

Parametric equations are sets of equations in which the Cartesian coordinates are expressed as explicit functions of one or more parameters.

Parametric to cartesian equation calculator