00:01
In this question, we will be talking about half -argument properties and graphs.
00:07
This question asks us to graph the function 10 times cosine of 5x times sine of 5x.
00:15
We're given that it's a sinusoid, and we want to find the equation of the sinusoid, and we're asked to check using algebra that this equation is indeed sinusoidal.
00:30
Now, i've graphed the function using this graphing software, though you should practice graphing by hand as well.
00:39
In this program, i see that using the default scale settings, which are equal for the x and y axes, this graph looks very narrow.
00:52
And so i want to zoom in, but just in the x direction.
00:55
I like this height, i just want it to be wider.
00:58
So i will use smaller numbers for x.
01:07
There we go.
01:09
That scale is much nicer.
01:12
Now i see that, well, i'm given that the equation is sinusoidal, so i know for sure, but i can very easily believe that because this looks very much like a sign function.
01:28
Indeed, it even intersects the y -axis at 0 ,0, like the sine function does.
01:38
So to find the equation of this single sinusoid, i can find the four significant properties.
01:47
The period, which is a measure of horizontal width, the amplitude, which is a measure of vertical width, the y intercept, which is a measure of the horizontal position, and the axis of symmetry, which is a measure of the vertical position.
02:09
So since this function looks like a sine function and it starts in the middle, it has the y intercept in the middle of the function, rather at peaks or valleys, i will start with sine of x.
02:26
If it started at a peak or valley, i would start with cos of x because that does the same thing.
02:33
It starts at a peak.
02:34
And so i noticed that my sign function is much wider than this function i have in green...