Converting Between Polar and Rectangular Equations

In class, we learned how to convert between polar and rectangular equations, mainly using substitution. Then we did some examples on the board just to see the different ways to convert between the two; some more sneaky then others.

Polar Graphing

Today we started class talking about how you need to be good at 30, 60, 90 and 45,45,90 triangles as well as being able to think even when things are not intuitive. (see first page of notes, shortest path is unexpected.)

We learned that a coordinate on a polar graph is labeled (distance, angle). Points on polar graphs have an infinite number of names. We also learned the formulas to convert polar points to rectangles points and vice versa. (this is all on the second page)

Plus we did a few examples. (see 3rd page)

Notes for February 17

We learned the basic parametric equations for circles, ellipses, and hyperbolas. We also did a problem using parametric equations to chart the path of a projectile.

February 16 Class Notes

Today in class, we discussed the different ways to write parabolas (vertex/standard form), learned how to find the focus and directrix, and drew graphs of parabolas.

More hyperbola and ellipse

Today in class we discussed more facets of ellipses and hyperboles. In other words, we learned how to write equations and draw both kinds of figures when given only a certain amount of starting information (ex. verticies and foci, center and foci, asymptotes, etc.).

-Also, we learned that "a" and "b" simply represent distances from the center of the figure.

-Where the asymptotes intersect on a hyperbola is the center of the hyperbola.

This is mostly useful information for our quiz on Thursday, Feburary 12th.

Conic Sections: Hyperbolas

In class today, we reviewed out second conic section: hyperbolas.

Hyperbolas act like the opposite of ellipses. Rather than adding the x and y terms in the standard form of the equation, we subtract them. Rather than subtracting a^2 and b^2 to find the foci, we add them.


We reviewed the "box" method of graphing in which we can draw a rectangle centered at (h,k) with length 2b and width 2a. This can be used to draw the desired asymptotes/vertices in the graph.

Pay close attention to the point-slope method to find the asymptotes and the way we decide what direction a hyperbola goes.


Finally, we reviewed how to change a messed-up equation in the form:

Ax^2+Bx+Cy^2+Dy+E=0

into standard form at the end of class(where A or C are negative).





Whenever you want to graph a hyperbola: label vertices, foci, asymptotes(show box work)

Monday Feb 9

We covered ellipses in class today. I am not going to post any notes today - instead I will just direct your attention to p640-641 in your textbook.

We will cover hyperbolas tomorrow and then review both on Wednesday. The quiz on Thursday will be over only those two shapes, as we will get to parabolas next week.

Class on Feb 5

There was a quiz today covering vectors, vector operations and vector applications.

There are no new notes today and the homework is a worksheet. The worksheet introduces vectors of the form <>.

notes Feb 4

Here are my notes for today. They were a little messier than usual, so I upped the scan quality just a bit.

The main concept is the dot product. The other big idea is the formula for finding the angle between two vectors.

There is a quiz tomorrow.

We went over three example problems in class today. Each is an application of vectors and could be considered "physics problems" as much as "pre-cal problems."

Note you can leave answers in component form unless specifically asked for the magnitude and/or direction of the vector.

notes for Feb 2

The only new concept I introduced in class today was the idea of the unit vector.

I did one physics-type example problem with velocity. The vector idea was that the velocity was given as magnitude and direction, and you need to break it down into horizontal and vertical components. Recall too that we have the old "projectile motion" model equation from our unit on quadratics.

We will go over several other physics-type problems in class tomorrow, including navigation and tension problems