![polar equation of a line through the origin graphing polar equation of a line through the origin graphing](https://d2mvzyuse3lwjc.cloudfront.net/doc/en/Tutorial/images/Polar_Contour/Polar_Contour_from_XYZ_data_00.png)
When a is greater than b, the petals are not tight (meaning they do not come back to (0,0) )but there are still k of them. We can also alter the shape of the graph by choosing values of and b that are not equal. Why does this change rotate the graph? (Discuss that cosine and sine equal 0 and 1 for different values of theta and why this results in a rotation.) We can change the equation from cos to sin and we will get a similar graph, but rotated. Below, we create a rose with petals of length 6. In the above examples, the length of the petals is two. If a = 0, we also get an n-leaf rose and the length of the petals is 1. When a = b, the sum of a and b gives us the "length" of our petals. In this situation we get an n-leaf rose where k indicates the number of leaves. Let's begin by looking at the equation when a = b. Polar equations can also be used to graph some relationships with are not easily defined in rectangular coordinates.
![polar equation of a line through the origin graphing polar equation of a line through the origin graphing](https://i.ytimg.com/vi/yS5_AezRE4A/maxresdefault.jpg)
The equation of line through the origin is also very simple: Theta = b where b is an angle in radians.įor example, below is the graph of theta = pi/4. The equation of a circle centered at the origin in polar coordinate is very simple: r = a where a is the radius of the circle.įor example, below is the graph of r = 3. If we think about graphing a polar equation on the x-y plane, then the angle theta is measured from the positive x-axis and r is the distance from the point (0,0) on the x-y plane.
![polar equation of a line through the origin graphing polar equation of a line through the origin graphing](http://publish.illinois.edu/ymb/files/2019/11/polar_cos2.png)
Polar equations define a relationship between an angle theta and a distance r. Polar Equations-A Brief Introduction to n-leaf Roses