.
This is the graph of f(x)=sinx:
![enter image source here]()
As you see, it has a period of 2pi and amplitude of 1..
This is the graph of f(x)=sin2x:
![enter image source here]()
As you can see, it has a period of pi and amplitude of 1. You have to divide the period of the sine function by the coefficient of your angle to get the period of your new function. In your problem, your angle is x and its coefficient is 2. When you divide 2pi by 2 you get pi.
Note that the amplitudes of both functions we graphed are 1.
This is the graph of f(x)=4sin2x:
![enter image source here]()
As you see, it has a period of pi and amplitude is 4 which tells you that if you have a coefficient behind the sine function, it gets multiplied by the amplitude of a normal sine function which is 1 and becomes the new amplitude, in this case 4.
This is the graph of f(x)=1+4sin2x:
![enter image source here]()
The constant that gets added to the function is the y-shift or vertical shift of the graph. In our problem, it is +1. This means that the graph of f(x)=4sin2x moves up by 1 unit in the y direction.
If you compare 4sin2x with 1+4sin2x, you will see that it has moved up one unit.
If you follow this process you can easily graph your trigonometric functions.
