00:01
The topic of this question is double and half argument properties.
00:07
This question asks us to plot the graph of 6 times sinex times cos x, find the equation of the sinusoid from the graph, and then check our answer using algebra.
00:28
So here i've plotted the graph in desmos, which is a free online graphing software.
00:37
That's very robust and handy.
00:40
And i've found that the period of this sinusoid that i see, which is the distance between similar x intercepts, by similar i mean the x intercepts that have a positive slope, the distance between those is pi.
01:08
And so my period is pi, and my amplitude, the height of the function, and the depth of the function above or below, the x -axis is 3, the y -coordinate here.
01:23
And so i know that my sinusoid can be written as sign of something.
01:35
It's obviously not sign of x because that's this purple function.
01:39
But i can scale, that is, stretch or compress my function, using multipliers a and b.
01:51
The a stretches the graph vertically, so stretches the amplitude, and b compresses the period horizontally.
02:02
Now, since sine of x has a period of 2 pi and an amplitude of 1, i want to get an amplitude of 3, like this graph, and a period of pi, i want to stretch the amplitude by 3, like this, and compress the period to be pi...