Amer said:what is the best way to graph in polar coordinates say
[tex]r = 3 - 5 \cos \theta [/tex]
is it to plot several points then make a curve between them or ?
Sudharaka said:Hi Amer,
Unless the curve given is a standard curve (circle, ellipse etc) or can be transformed into a standard form, we have to plot it by marking points. I drew your curve using Maxima.
http://imageshack.us/f/337/figure.png/
Amer said:thanks so i need to plot some points. ok
Polar coordinates are often used to graph equations or data that involve circular or rotational patterns. They allow for a more intuitive understanding of these types of functions and can also make it easier to identify symmetries and special points on a graph.
To convert from Cartesian coordinates (x,y) to polar coordinates (r,θ), you can use the formulas r = √(x²+y²) for the distance from the origin to the point and θ = arctan(y/x) for the angle formed by the positive x-axis and the line connecting the origin to the point.
No, polar coordinates are only used for 2-dimensional graphs. To graph 3-dimensional objects, you would need to use a different coordinate system such as cylindrical or spherical coordinates.
A polar graph uses polar coordinates, which are based on a distance from the origin and an angle from the positive x-axis, while a Cartesian graph uses Cartesian coordinates, which are based on a distance from the x-axis and y-axis. Polar graphs are typically used for circular or rotational functions, while Cartesian graphs are used for linear functions.
To plot a point in polar coordinates, you first locate the distance from the origin (r) and then rotate that distance by the specified angle (θ) from the positive x-axis. You can then plot the point at the resulting (x,y) coordinates. Alternatively, you can also use the polar gridlines on a polar graph paper to plot the point directly.