How to draw trigonometric graphs. (1 Viewer)

[asdfqwerty]

Hey everyone!

Can somebody please teach me how to draw trigonometric graphs in terms of pi and its features (eg. what happens to the amplitude and period when you multiply the function like (2cosx, 3sinx, 4tanx etc) or add it with an integer (eg. cox+3) etc).

My teacher didn't really cover this in the preliminary course when we did trigonometry and I can't do questions on trigonometric functions atm because I don't know what to draw.

Thanks!

 

[deswa1]

Its like any other graph. Say if you've graphed y=cosx. If you want to graph y=2cosx, then at every y value you multiply it by two. This means that the amplitude will double, but the period will remain the same because obviously when cosx=0, 2cosx will also equal zero. The same principle applies for 3sinx etc.

With y=cosx+3, what that means is that at every y value of y=cosx, you add three to it. For example, when x=pi/2, cosx=0. Therefore when x=pi/2, y will equal 3 in the graph y=cosx+3.

Pretty much, when you add or subtract you shift the whole graph up or down and when you multiply, you keep the graph in the same position but you 'strecth' it either upwards or downwards depending on what number you multiply by.

It might be useful to use a few of those online graphing software and graph both of those functions simultaneously so you can get a hang of what's happening.

 

[Nooblet94]

Multiplying the function by a constant will increase the amplitude of the wave as you can see in the link below.
http://www.wolframalpha.com/input/?i=plot+y%3Dsinx+and+y%3D2sinx+and+y%3D3sinx

Adding a constant will shift the graph up, down, left or right depending on where you add it. It's the same as shifting any other graph.
http://www.wolframalpha.com/input/?i=plot+y%3Dsin%28x%2B1%29+and+y%3Dsinx%2B1

Replacing x with x+1 will shift the graph 1 unit to the left, while replacing it with x-1 will shift it one unit to the right. In general, replacing x with x-k will shift the graph k units to the left. Similarly, replacing y with y-k will shift the graph k units upwards. (Just to clarify, k is just some constant, it can be positive or negative)

 

[Carrotsticks]

Hey everyone!

Can somebody please teach me how to draw trigonometric graphs in terms of pi and its features (eg. what happens to the amplitude and period when you multiply the function like (2cosx, 3sinx, 4tanx etc) or add it with an integer (eg. cox+3) etc).

My teacher didn't really cover this in the preliminary course when we did trigonometry and I can't do questions on trigonometric functions atm because I don't know what to draw.

Thanks!

• If I have , A determines the amplitude of the curve. This is how high it goes up and down. The larger A is, the higher it goes up and down.
  
• If I have , A determines how much I shift the original cos curve up and down. If , then the entire curve is shifted up by 1 unit.
  
• If I have , A determines how 'fat' or 'skinny' my curve is. If A is larger, then the curve is skinner. If A is smaller, then the curve is fatter. If , then the curve is twice as skinny. If , then the curve is twice as fat.
  
• If I have , A determines how much I shift the original curve sideways. If , then the curve is shifted to the right by units.
  

What I listed above is all you need to know. Combine all of these transformations to break down a big question.

For example, if I was asked to draw the curve , then this is what I would do (if I'm still learning. Eventually, you will learn to do it in 1 go):

1. Change the question to make it become This is because you want to make the coefficient of X become 1. Transformations are easier to spot this way.

2. Draw the original cos curve, but with amplitude 2 instead of 1.

3. Shift it to the right by units, since the inside of the bracket is .

4. Shift down by units.

5. Squash my curve to make it twice as skinny (so within the same interval, it should have double the number of periods)

6. Enjoy new curve.

The key do getting these questions right is to do 1 transformation at a time. Many students try to combine several transformations at once, and end up screwing up the question. Although this method takes up a bit more time, it guarantees that you will get full marks.

Eventually, you will be able to skip steps once you master these techniques.