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Numerade Educator

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Problem 2 Medium Difficulty

Graph the functions for one period. In each case, specify the amplitude, period, $x$ -intercepts, and interval(s) on which the function is increasing.
(a) $y=3 \sin x$
(b) $y=\sin 3 x$

Answer

$$\begin{aligned}&\text { amplitude }=1, \text { period }=\frac{2 \pi}{B}=\frac{2 \pi}{3}, \quad B=3\\&x \text { -intercepts }=0, \pi / 3,2 \pi / 3\\&x \text { increases in }(0, \pi / 6) \text { and }(\pi / 2,2 \pi / 3)\end{aligned}$$

Discussion

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Top Algebra Educators
Catherine R.

Missouri State University

Anna Marie V.

Campbell University

Alayna H.

McMaster University

Michael J.

Idaho State University

Video Transcript

So for part A, we're gonna talk about why is equal to three sighing x So four thing is P amplitude is he cloaked in city and the P eight is equal to two pipe. So in order to draw the craft, what we need to do this half these points here. So this would be pie or two. Why pi over two and to buy and the amplitude history. So on the y axis, the craft will not go above three and it will not go below negative. So we have set up our axes, that straw graph. So this is what the craft would look like over that control. Now, the next thing is, we want to talk about the X intercepts. So there are three X intercepts at X is equal to zero, and X is equal to high and at X is equal to two pi and then increasing over working toe. So it's increasing over, uh, ex going from zero to pi or two and also from X going from three pi over 22 Hi due to play. So that's the part it let's talk about part B. So Part B say's Why is equal to sign the X so far. Thing is, what's the amplitude? So the aptitude would now be one and the pdf would be two pi divided black city or that would be two pi or three. So in order to set the craft up, we have Ah, this would be to pi over 62 pi over six weeks simplifies to pie or fee. So this would be worth me. This would be chi over six and this would be two pi over three. So then the AM patron is one and this would be negative one. So the value of the why I will not go apartment well on these two nights get strong the craft. So this is what it would look like now, uh, the X intercepts. So there's a X is equal to zero. There's X is equal to pi over three and their sex is equal to two pi or three. And then the function is increasing over what intervals. So the function is increasing over ex going from zero to pi over six and the other interval or which is increasing, would be from they were to to two pi or three

Other Schools
Top Algebra Educators
Catherine R.

Missouri State University

Anna Marie V.

Campbell University

Alayna H.

McMaster University

Michael J.

Idaho State University