Precal Blog

Alrighty so we started class with a Worksheet that was basically practice of drawing csc and cos graphs (preferably without the “training wheels” of a sin or cos graph.) The we were confronted with the problem of how to graph a tan function. We then discussed how a tan graph is made from using both cos and sin graphs. Using the following logic.

So if you were to find what sin(0) (I can’t get pheta so pretend thats what zero is) equals it would be Sin (0) V/R your could then solve for V and get V= Sin(0)*R. Then if you would do the same for cos(0) it would be Cos(0) = U/R. Then solve for U and you get U=R*Cos(0). YOu also can determine what tan is. tan(0) is V/U. You can plug in what U and V equal to get R*Sin(0)/R*cos(0). The R’s cancel out so you are left with Sin(0)/Cos(0). YOu then get the graph.

Now we must find out what point are in the graph of tan. We know that there will be asymtopes when cos equals 0 because you cannot divide by a zero. Also when sin=0 it will also be zero becasue any number divided by 0 equals 0. And finally we know that When Cos and Sin share a point (every 45 degrees) tan will equal 1 since any number divided by itself will equal 1. If cos and sin are the same number but one is positive and the other is negative then the point will be negative one. We then can also use the same logic we used in other graphs and that the tan will get larger and larger as cos gets smaller and smaller because dividing by a small number equals a large number. Later we will learn how to transform these graphs. It is important to remember that the points where y equals 0 is always between the asymtopes. Lastly we were assigned to read 3-3. Thats all we did today

the next scribe will be Gerorge