Functions and periods

[clobber]

So these 3 graphs, need the functions of them and their periods. Tried the last one they look similar 2 of them so not fully sure with them

function: cos ?
period: 2 pi?

function: sin
period: 2 pi

function: tan?
period: pi?

 

[Muddyakka]

These are the graphs of y = sin(x), cos(x), and tan(x).

It is a good idea to understand how these graphs can be translated, and/or stretched/compressed, on desmos.

e.g. Given sinx, how does sin(2x) change?
Or
e.g. Given tanx, how does 2tan(x/2) +1 change?

A period of a graph is the distance between two peaks (or between any 2 matching points that contain a full cycle) and is affected by the co-efficent of x. I will leave it to you to find this relationship. ?

 

[Otis]

… need the [function names and] periods … not fully sure…
[1st] function: cos … period: 2 pi
[2nd] function: sin … period: 2 pi
[3rd] function: tan … period: pi

Hi clobber. You are correct!

… they look similar 2 of them …

Yes, the curves of sin(x) and cos(x) have exactly the same shape, when plotted using identical axes scales. Your sine graph appears compressed, compared to your cosine graph, because the x-axis on the sine graph has been scaled down (that is, a much shorter distance represents Pi radians, compared to the cosine graph).

Even though the sine and cosine curves have the same shape, their plots are offset horizontally from one another. If we shift the cos(x) graph Pi/2 units to the right, we get the sin(x) graph. Likewise, shifting the sin(x) graph Pi/2 radians to the left gives us the cos(x) graph.





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