Question

the graph of which of the function has an amplitude of 2 and a period of 4pie?

Answer 1

To find the amplitude of a sine or cosine, you just look at the number in front of the function. That is, if:
\[f(x) = A \sin(x)\]
Then A is the amplitude (If it's negative, you can just use the absolute value)

Answer 2

For periodic functions like sine and cosine, we can find the period by using the frequency in the function, and what the period would be if that frequency were 1 (you'll need to know these, or look them up).

For instance, if given:
\[f(x) = A \sin(\omega x - \phi)\]

The period would be the period of sin(x) divided by the frequency.

sin(x) has a period of 2Pi, so the period of f(x) would be:
\[\tau = \frac{2 \pi}{\omega}\]

Answer 3

Now, if you don't have a function given to you, but are looking at a graph, you can see these things pretty easily. An amplitude is the "height" of the wave, measured from the center point. From the heighest point of the wave to the lowest, is two times the amplitude. So, looking at a graph, you can see if it has the correct amplitude.



Does that make sense?