Algebra/Trig Review - Pauls Online Math Notes - Lamar University

Algebra/Trig ReviewTo do this problem it will help to know that tangent (and hence cotangent) is also aperiodic function, but unlike sine and cosine it has a period of π .tan ( x+ π n) = tan ( x)n = 0, ± 1, ± 2, cot x+ π n = cot x( ) ( )So, to do this problem let’s note that 4 π π= π + . Therefore,3 3⎛4π ⎞ ⎛ π ⎞ ⎛π⎞tan ⎜ ⎟= tan ⎜π+ ⎟= tan ⎜ ⎟=3⎝ 3 ⎠ ⎝ 3⎠ ⎝ 3⎠Trig Evaluation Final ThoughtsAs we saw in the previous examples if you know the first quadrant of the unit circle youcan find the value of ANY trig function (not just sine and cosine) for ANY angle that canbe related back to one of those shown in the first quadrant. This is a nice idea toremember as it means that you only need to memorize the first quadrant and how to getthe angles in the remaining three quadrants!In these problems I used only “basic” angles, but many of the ideas here can also beapplied to angles other than these “basic” angles as we’ll see in Solving Trig Equations.Graphs of Trig FunctionsThere is not a whole lot to this section. It is here just to remind you of the graphs of thesix trig functions as well as a couple of nice properties about trig functions.Before jumping into the problems remember we saw in the Trig Function Evaluationsection that trig functions are examples of periodic functions. This means that all wereally need to do is graph the function for one periods length of values then repeat thegraph.Graph the following function.1. y = cos( x)SolutionThere really isn’t a whole lot to this one other than plotting a few points between 0and 2π , then repeat. Remember cosine has a period of 2π (see Problem 6 in TrigFunction Evaluation).Here’s the graph for −4π≤ x ≤ 4π.© 2006 Paul Dawkins 53http://tutorial.math.lamar.edu/terms.aspx