Our Discord hit 10K members! 🎉 Meet students and ask top educators your questions.Join Here!

Like

Report

Numerade Educator

Like

Report

Problem 4 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) $y=\cos (x / 2)$
(b) $y=-\frac{1}{2} \cos (x / 2)$

Answer

(a.) amplitude $=1,$ period $=4 \pi$(b.) amplitude $=-1 / 2,$ period $=\frac{2 \pi}{B}=\frac{2 \pi}{1 / 2}=4 \pi$

Discussion

You must be signed in to discuss.
Top Algebra Educators
GH
Grace H.

Numerade Educator

Anna Marie V.

Campbell University

Kayleah T.

Harvey Mudd College

Michael J.

Idaho State University

Video Transcript

so we have for part a Why is equal to co sign off X over two. The amplitude would be one, and the P AED is two pi divided by 1/2, which was before. So let's draw this craft on the x axis would come but pie to pie, the pie and four pi and the aptitude is one. So on the why accessed in value. So why I will not go above bicycle to one. They will not go below bicycle connected one. So the graph would look like this. That's not looking pretty. So this is what the graph would look like. So here's the graph off course sine X over two. Now the X intercepts there are three. There are two X intercepts, and those X intercepts are attacks is too high and at X is equal to three pie. And then the function is increasing for the interval for X values between two pie and for pie. So that's part eight. Now let's talk about party. So for part B D. Question is, why is equal to negative 1/2 course sine X over two. So the abd acute that now is 1/2 and the pdf is still too pie divided by 1/2, which is four point. So no need to draw the crap and let set up our X axis pi to pie three and four pi. But now the why values will be between negative water were too and positive what over two. And this is a negative course and graph, which means you take the course and graph and reflected over the X axis. So the graph would be like this. Yeah, the X intercepts are still the same pie, and it was equal to buy. And now the doubles over Wasti craft is increasing, so the craft is increasing over X values from 0 to 2 pi, and that's the only in Kabul.

Other Schools
Top Algebra Educators
GH
Grace H.

Numerade Educator

Anna Marie V.

Campbell University

Kayleah T.

Harvey Mudd College

Michael J.

Idaho State University