The most popular two-dimensional coordinate system is Cartesian coordinate system. It consists of a fixed point (point of origin) and two orthogonal* (the angle between them is 90 degrees) straight lines (coordinate axes) intersecting in this point. Each coordinate axis is given a direction in which its values grow and a scale. One coordinate axis (X-axis) is called abscissa axis, another (Y-axis) is called ordinate axis. A point in Cartesian coordinate system is specified by 2 coordinates (x; y). *Sometimes it is more convenient to use a system with an angle between the coordinate axes different from 90 degrees (such systems are called non-orthogonal).	Cartesian coordinate system
In Cartesian system functions may be given as dependence y = f(x) or x = f(y). For example, the parabola is given as y = x2. The node points of this function are presented in the table (built manually or using a software product): x -3 -2 -1 0 1 2 3   y = x2 -32 = 9 4 1 0 1 4 9   This points are drawn on the graph and linked with lines.	Parabola y = x2
The dependence may be given in an implicit way as F(x; y) = 0 (when it is hard or impossible to express one coordinate through another). For example, the circle with the center at point (0; 0) is given as x2 + y2 = R2, where R is the radius of the circle.
Another way to specify a function is to express both its coordinates as functions of some parameter: x = f(t), y = g(t). For example, the ellipse with center at point (0; 0), horizontal radius Rh = 9 and vertical radius Rv = 7 is given as x = 9*cos(t), y = 7*sin(t). The node points of this function are (parameter t changes with step 45 degrees from 0 to 360 degrees): t 0 45 90 135 180 225 270 315 360   x = 9*cos(t) 9 6,39 0 -6,39 -9 -6,39 0 6,39 9   y = 7*sin(t) 0 4,97 7 4,97 0 -4,97 -7 -4,97 0	Ellipse
Another frequently used two-dimensional coordinate system is called polar system. It is a curvilinear coordinate system. It consists of a fixed point (pole), a number of circles with center at the pole and a number of rays drawn from the pole. A point in polar coordinate system is given by intersection of one of the circles and one of the rays and is specified by 2 coordinates: R - the radius of the circle and p (polar angle) - the angle between the polar axis (one of the rays; usually the ray drawn to the East) and the ray containing the point.	Polar coordinate system
In polar system functions are usually given as dependence R = f(p). For example, the Archimedean spiral is given as R = p/36. The node points of this function are (parameter p changes with step 45 degrees from 0 to 360 degrees): p 0 45 90 135 180 225 270 315 360   R = p/36 0 1,25 2,5 3,75 5 6,25 7,5 8,75 10	Archimedean spiral
You can build any two-dimensional functions given in Cartesian/polar coordinate systems or parametrically using Tavrida Scientific Calculator (all above sample graphs are build with our program). You can build any number of functions on one graph. You simply create the two-dimensional graph, add functions (for example, y = x^3, x = 1, R = -p/36 and [x = 4*cos(t): y = 6*sin(t)]) and get the result (see sample graph to the right). Click here to download Tavrida Calculator.	Sample graph