# Nates notes

The superior aspect of the buttock ends at the iliac crestand the lower aspect is outlined by the horizontal gluteal crease. The gluteus maximus has two insertion points: The masses of the gluteus maximus muscle are separated by an intermediate intergluteal cleft or "crack" in which the anus is situated. The buttocks allow primates to sit upright without needing to rest their weight on their feet as four-legged animals do.

Due to the nature of the mathematics on this site it is best views in landscape mode.

If your device is not in landscape mode many of the equations will run off the side of your device should be able to scroll to see them and some of the menu items will be cut off due to the narrow screen width. However, as we will see, this is not always the easiest coordinate system to work in.

So, in this section we will start looking at the polar coordinate system. Coordinate systems are really nothing more than a way to define a point in space. This is shown in the sketch below. This is not, however, the only way to define a point in two dimensional space.

Coordinates in this form are called polar coordinates. This leads to an important difference between Cartesian coordinates and polar coordinates. In Cartesian coordinates there is exactly one set of coordinates for any given point.

In polar coordinates there is literally an infinite number of coordinates for a given point.

For instance, the following four points are all coordinates for the same point. In the second coordinate pair we rotated in a clock-wise direction to get to the point. These four points only represent the coordinates of the point without rotating around the system more than once.

If we allow the angle to make as many complete rotations about the axis system as we want then there are an infinite number of coordinates for the same point. In polar coordinates the origin is often called the pole.

Well start out with the following sketch reminding us how both coordinate systems work. Summarizing then gives the following formulas for converting from Cartesian coordinates to polar coordinates. Example 1 Convert each of the following points into the given coordinate system.

Show Solution This conversion is easy enough. All we need to do is plug the points into the formulas. We can also use the above formulas to convert equations from one coordinate system to the other.

Example 2 Convert each of the following into an equation in the given coordinate system.

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Show Solution This one is a little trickier, but not by much. However, there is no straight substitution for the cosine that will give us only Cartesian coordinates. This leads us into the final topic of this section. Lines Some lines have fairly simple equations in polar coordinates.