Precal Blog

So I think 2nd hour is a little behind 3rd so you have probably seen tan graphs before this post, so if you need visuals you can just look at past blogs.

We all know that tangent is defined as opposite over adjacent or v/u. Another way we can define tangent is by using sin and cos. By solving for v in the equation sinX=v/r (X means theta) and solving for u in the equation cosX=u/r, you can put the values into the tanX=v/u equation. Giving you tanX=(r*sinX)/(r*cosX). The r’s cancel out and your left with tanX=sinX/cosX.

Now that you have tangent defined as sin/cos, it makes it a little easier to graph. Whenever sinX=0 (ex. X=0, +-180, +-360…), tanX=0 because 0/cosX will equal 0

You can easily find the vertical asymptotes because whenever cosX=0 (ex. X=+-90, +-270, +-450…) , tanX will be undefined (sinX/o).

When sinX and cosX are opposites, tanX=-1. When sinX=cosX, tan=1.

So that is the basic tangent graph. The next step would be to learn how to transform tangent graphs! I know it sounds scary and if you don’t quite get how to do it right away, don’t worry because Mr. Bieniek said tangent graphs are one of the hardest lessons.

The next scribe will be Stefan V.