# How to graph cosine and sine

1. Oct 14, 2007

### PHK

I need help on graphing cosine and sine functions. i know how to read a graph and come up with the equation but i dont know how to do it the other way around. i want to be able to graph something like y=-2+2cos0.5x

2. Oct 14, 2007

### futurebird

3. Oct 15, 2007

### Gib Z

For any function in general, where $y= a \cdot f( b (x-c) ) + d$, to graph it we work from the inside out.

So first graph f(x) as normal. Then move that graph c units to the right. If it is (x+c) instead, then c units to the left.

Then squeeze the shifted graph by a factor of b times horizontally. If like in this case, its less than 1, write it in the form 1/b (b is 2 for your example). For when its in the form 1/b,
then stretch it by a factor of b times horizontally.

Then stretch the whole thing vertically by a factor of a. If a is negative, also flip the graph upside down. Similar thing, if a is less than one, rewrite the coefficient as 1/a. Then squeeze vertically by a factor of a.

Now just must that up by d units, or if d is negative, down d units.

Its really must easier to put into practice and to understand than it looks.

For this one, get the normal Cosine graph, stretch it horizontally by a factor of 2. Eg where the normal cosine graph first intercepts the x axis at pi/2, it is now at pi.

Then, stretch it up and down by a factor of 2. So all the points that it is 0 stay the same, where they are 1 they becoming 2, and where they were -1 they become -2.

Now just shift that down by -2. So where they were -2, it becomes -4, and where they were 2, it becomes 0.

=]

4. Oct 15, 2007

thanks i got