# The Graphs Of Trigonometric Functions Assignment Help

**The Graphs of the Trigonometric Functions**

### What is Graphing Trigonometric Functions?

To graph sin x and cos x, look at the unit circle to help you get the corresponding points. csc x and sec x are the reciprocals of sin and cos respectively, with tan x = sin x/cos x and cot x = cos x/sin x.

If a function has a coefficient in front of it, the absolute value of that coefficient is the AMPLITUDE of the function. If the variable has a coefficient in front of it, we call that variable b with the PERIOD defined as 2pi/b or 360/b depending on the unit of measure for the angles(for all but tan/cot where the period is pi/b or 180/b). If the argument of the function has a number added or subtracted (such as 2x-90), we factor that expression and the constant left over is the PHASE SHIFT--a description of how the graph is shifted horizontally. Finally if there is a constant added at the very end to the argument, like f(x) = sin(x) +3 , the constant is the VERTICAL DISPLACEMENT--describing the vertical shift of the function.

### Why study Graphing Trigonometric Functions?

Trigonometric function are by far the most used elements in any mathematical study. You may very well know how to solve equations consisting of a trigonometric function, but graphing a trigonometric function gives you a deeper understanding of how a function changes its values when moving from one point to another.

This may seem very simple and straightaway in case of singular trigonometric functions, but when you combine more than one trigonometric functions into a single expression, you can very well judge the behaviour of the function on a graph, simply by knowing the graphical representations of the primitive functions. This may sometimes even help in getting to the answer earlier.