Transformations of graph of y = sin x

ExitMusic

Graphs HERE

:confused:

What are the equations of these graphs? (in the form y = a sin (bx) + c) (transformations of the graph y = sin x)

Reply 1

Cexy

In the second one, you can see that there are 6 repetions of the graph, where there would normally only be a quarter of a period between 0 and 90 - so it's oscillating 24 times faster. So you have something with

sin(24x)

in it. Also you can see that the graph goes from 45 at its minimum, to 145 at its maximum (spanning 100 units) whereas a normal sin graph goes from -1 to 1 (spanning two units). So you have

50sin(24x)

Then notice that the graph is a mirror image to what you'd expect, as 'sin' normally goes upwards from the origin. So you're looking for a

-50sin(24x)

And finally, sin(0) is normally zero, but here it's 90, so your final equation for the graph is

y = -50sin(24x) + 90

Reply 2

the bear

the first one seems to be

-3sin(x/3) -1

the period is 3*normal hence the division by 3 . the amplitude is 3*normal hence the multiplication by 3. it is upside down hence the negative at the start. it has been moved down 1 unit hence the -1 at the end.