11/23 Notes

In class, we worked with trigonometry identities. When you have a trig equation, you want to first look to do algebra: factor, expand, or get a common denominator. Second, look for trig IDs to use. We learned definitions ie sec(x)=1/(cos(x)). We also looked at the pythagorean IDs: cos^2(x) + sin^2(x)=1, 1+tan^2(x)=sec^2(x), cot^2(x)+1=csc^2(x). We also studied complement IDs (ex. cos(x)=sin((pi/2)-x))and reflection IDs (ex. sin(x)=(pi-x)). We applied these IDs to simplify equations and expressions.

11/17 class notes

Today in class we talked about inverse trigonometric functions, like arcsin etc. The main concept we covered was the ambiguity of the number of solutions for these functions. In other words, how do we restrict arcsin etc. to only produce one solution? (for example if you plugged in arcsin= .5 to your calculator how could you insure that it would give you the answer 30 degrees rather than 390, - 330, etc?) Well what we do is restrict the domain and range. In the chart in the notes it lists the different domain and range restrictions for the different functions. The reason we have to insure they only have one solution is that if they had multiple they would not be functions anymore (aka more than one output).

These notes are about graphing tan

November 9 - Trig Graphs

Today in class we started by reviewing the basic facts about the graphs of y = a cos (bx) and y = a sin(bx). We moved on to an example of writing an equation for a given trig graph. You need to consider how to find the amplitude (a = (Max - min) / 2), the vertical shift (k = (Max + min) / 2), and b by recognizing the period (period = 2π / b). Once those values are determined, consider the graph of y = a cos (bx) + k. Finally, determine how that graph can be shifted to "overlap" the given graph to obtain a final equation of the form y = a cos(b(x - h)) + k.

The same process can be used to obtain an equation of the form y = a sin (b(x - h)) + k. Note, there is not one unique answer in any case.

Sine and Cosine Curves

First off, I would like to tell everyone I'm sorry I didnt get this on here sooner if y'all needed. Anyway, Friday in class we discussed the graphs of both sine and cosine graphs. We covered the topics of period and amplitude as well as the standard form of an equation for said graphs.

Today we continued our discussion on trig functions, however we incorporated reflections and the Pythagorean theorem. We learned how to find the sine, cosine, and tangent of theta when it is reflected across the x-axis, y-axis, or origin. We used the Pythagorean theorem to find the missing side of a triangle and the equation of a circle (see HW notes).

Notes, 11/3/09

Main Topics of Lesson...

• unit circles
• the coordinate (cos of theta, sine of theta)
• the four other trigonometric functions
• reflecting theta across the axes and origin

Notes follow...

Notes, 11/2/09

Today we began to move into trigonometry by looking at angles and their measures. The two units of measurements for angles are degrees and radians. It should be noted that one radian is the measure of the angle formed at the center of a circle when the arc length is the same as the radius. This comes out to approximately 57.1 degrees. (see notes for picture) We also looked at how to determine arc length, as well as supplementary and complementary angles. Notes below.