How do you graph sine and cosine functions when it is translated?
2 Answers
I think you'll find a useful answer here: http://socratic.org/trigonometry/graphing-trigonometric-functions/translating-sine-and-cosine-functions
Vertical translation
Graphing
In this case we start with a number (or angle)
This gives us a final
This will translate the graph up if
or down if
Examples:
graph{y=sinx [-5.578, 5.52, -1.46, 4.09]}
graph{y=sinx+2 [-5.578, 5.52, -1.46, 4.09]}
graph{y=sinx-4 [-5.58, 5.52, -5.17, 0.38]}
The reasoning is the same for
graph{y=cosx [-5.578, 5.52, -1.46, 4.09]}
graph{y=cosx+2 [-5.578, 5.52, -1.46, 4.09]}
Horizontal Translation
One way to think about horizontal translations of a function is to think about the value of
We know the graph of
To graph
Now, what value of
So "
graph{y=sin(x-4) [-0.498, 7.295, -2.302, 1.596]}
To graph
That will be
So, "
(For the graph below, remember that
graph{y=sin(x+pi/3) [-3.02, 1.845, -1.192, 1.241]}
To start the graph of
Cosine
The reasoning for graphing
graph{y=cos(x+pi/3) [-3.02, 1.845, -1.192, 1.241]}