- #1
hale2bopp
- 21
- 0
When plotting graphs in polar coordinates, how does one know when to make the graph sharp (at θ=0) (as in for the graph for r=1-cosθ) as opposed to a dimple (r=3/2 + cos θ) ?
To convert cartesian coordinates (x,y) to polar coordinates (r,θ), use the following formulas:
r = √(x² + y²)
θ = arctan(y/x)
To plot a point (r,θ) in polar coordinates, start at the origin (0,0) and move r units in the direction of θ. Then, draw a line connecting the origin to the point to create a polar graph.
The scale for a polar graph is determined by the maximum value of r and the number of units on the graph. For example, if the maximum value of r is 10 and the graph has 8 units, each unit on the graph would represent 1.25 units in polar coordinates.
To graph equations in polar coordinates, first convert the equation to polar form using the formulas:
x = rcos(θ)
y = rsin(θ). Then, plot points on the graph using the converted values and connect them to create the graph.
Yes, you can use negative values for r in polar coordinates. This indicates that the point is located in the opposite direction of θ from the origin. For example, a point with coordinates (-3,π/2) would be located 3 units to the left of the origin in the direction of π/2 radians.