Question 37 (1 point) The partial graph of a sinusoidal...

Question 37 (1 point) The partial graph of a sinusoidal function is shown below. A possible equation of the graph is ________. y = \sin\left(\frac{2\pi}{k}x\right) y = \sin\left(\frac{\pi}{k}x\right) y = \sin\left(\frac{4\pi}{k}x\right) y = \sin\left(\frac{k}{2}x\right)

Transcript

00:01 In this problem, we have y equals the sign of one -half x plus pi over four.

00:09 Thinking about the pieces here, we're going to start looking by analyzing the amplitude.

00:14 The amplitude here is going to be the absolute value of the number multiplying by the outside of the function.

00:20 In this particular case, it's going to be one, which means it's going to go up one and down one from my midline.

00:26 And traditionally, a positive sign curve will look like this.

00:29 So it's going to start on the midline, go up, midline, down, midline.

00:34 So this will be a pretty traditional amplitude for this new graph as well.

00:40 Looking at the period, the period is calculated by taking 2 pi and dividing by the frequency.

00:47 The frequency is the coefficient of x here, which is this 1⁄2.

00:51 So i'm going to be doing 2 pi divided by 1⁄2, which is the same as 2 pi times 2, which in this case is 4 pi.

01:00 So the distance from the starting point to the last point will be 4 pi for one cycle.

01:06 Finally, we're going to take a look at the phase shift.

01:09 And in this case, it will be the opposite movement of what's happening inside of the function.

01:13 And so in this case, it's negative pi over four.

01:16 So we're going to go to the left, pi over four.

01:21 Now, to get a good graph here, because i'm not really sure where i'm getting a shift to the left and i am changing its period, and what i do is i like to start by putting my x -axis in and putting one, two, three, four, five equally spaced tick marks so that my picture looks pretty and i can get it all matching up nicely.

01:42 Then i like to use a transformation table to label my intervals.

01:46 Once i have my intervals labeled, then i can put my y -axis in.

01:50 So in this case, i'm looking at a traditional sign curve.

01:53 So if i didn't change it at all, according to the unit circle, it would be 0 ,0, pi.

02:00 Over 2 -1, high, pi -0, et cetera, et cetera, et cetera.

02:08 And that will give us my pattern of what's going on.

02:11 Now, anything on the outside, multiplying times the trig and adding or subtracting to the trig will affect my output...

Question

Question 37 (1 point) The partial graph of a sinusoidal function is shown below. A possible equation of the graph is ________. y = \sin\left(\frac{2\pi}{k}x\right) y = \sin\left(\frac{\pi}{k}x\right) y = \sin\left(\frac{4\pi}{k}x\right) y = \sin\left(\frac{k}{2}x\right)

Please give Ace some feedback