Thread: Drawing trigonometrical graphs

1. Drawing trigonometrical graphs

I need some help with drawing y=sin(x) and y=cos(x) graphs. For example I have y=sin(x + pi/6) and y=cos(3x). How to draw graphs of these trigonometrical functions? How to find out points x and y to draw? I know that first step is finding period of the function. But I don't know how to do that too. So, could someone explain me this?

2. Originally Posted by vykis
I need some help with drawing y=sin(x) and y=cos(x) graphs. For example I have y=sin(x + pi/6) and y=cos(3x). How to draw graphs of these trigonometrical functions? How to find out points x and y to draw? I know that first step is finding period of the function. But I don't know how to do that too. So, could someone explain me this?
You must learn the basic shape of $\sin(x)$ and $\cos(x)$. You can then apply transformations as with any graph.

For example the graph of $y = \sin \left(x+\frac{\pi}{6}\right)$ is the same shape as $y=\sin(x)$ but moved by $\frac{\pi}{6}$ units to the left

3. So if there is y=sin(3x), it means that the graph is three times tightened? I mean that if in y=sin(x) the graph crosses the x-axis in ${\pi}$, it will cross it in point $\frac{\pi}{3}$ in y=sin(3x)? And for example if there is y=sin(x/5), it means that the graph is five times strained? It will cross x-axis in $5{\pi}$?

And waht about cos? Is the way of drawing it the same?

4. Originally Posted by vykis
So if there is y=sin(3x), it means that the graph is three times tightened? I mean that if in y=sin(x) the graph crosses the x-axis in ${\pi}$, it will cross it in point $\frac{\pi}{3}$ in y=sin(3x)? And for example if there is y=sin(x/5), it means that the graph is five times strained? It will cross x-axis in $5{\pi}$?

And waht about cos? Is the way of drawing it the same?
That's right for the stuff about sin(ax)

cos(x) is a known graph but the transformations apply equally-for example cos(3x) will also be 3 times tightened

EDIT: see the attached graphs for how it would look for various transformations - the first one is from $\sin(x)$ and the second based on $\cos(x)$

EDIT II: You may notice that the graph of $\sin(x)$ is $\frac{\pi}{2}$ to the right of the graph for $\cos(x)$. Can you deduce a relationship between sin(x) and cos(x) based on this information?

Spoiler:
$\sin(x) = \cos \left(x - \frac{\pi}{2}\right)$. This can also be shown by using the trig addition formulae