## Announcements

In order to review the topics that were on Exam #2, and to give you a chance to improve your exam score, I will give a series of make-up exam exercises that you can use to replace some of your Exam #2 scores. The first one will be Monday at the end of class, and will cover the quadratic formula and complex numbers (similar to #3 and #5 on Exam #2). I have reopened those WebWork sets so that you can complete those exercises if you didn’t previously.

WebWork:

• ComplexNumbers – due Mon May 6
• Graphs-Graphs of Quadratic Equations – due Tues May 7
• Trigonometry-Right Triangles Trigonometric Ratios – due Wed May 8

Schedule for the remainder of the semester:

## Topics

We introduced equations of circles, and did some examples from the “Graphs of Quadratic Equations” WebWork.

First we looked at circles centered at (0,0), which have equations of the form

x^2 + y^2 = r^2

where r is the radius of the circle (note that the equation comes from the Pythagorean Theorem–it is satisfied by points (x,y) that are distance r from the (0,0)!)

Next we looked at how the center can be “shifted” to a different point:

Two examples from the WebWork; in the second example we have to “complete the squares” on the x-terms and y-terms in order to put it in “standard form” so that we can find the center and radius:

We then started trigonometry. We reviewed the definitions of the trig ratios (sine, cosine, tangent) and their reciproicals (cosecant, secant, cotangent):

We did some examples from the “Trigonometry-Right Triangles Trigonometric Ratios” WebWork: