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Problem 3 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) $y=\cos 2 x$
(b) $y=2 \cos 2 x$

Answer

(a.) amplitude $=1,$ period $=\frac{2 \pi}{B}=\frac{2 \pi}{2}=\pi$
$x$ -intercepts $=\pi / 4,3 \pi / 4$
$x$ increases in $\left(\frac{\pi}{2}, \pi\right)$
(b.) amplitude $=2,$ period $=\frac{2 \pi}{2}=\pi$
$x$ -intercepts $=\frac{\pi}{4}, \frac{3 \pi}{4}$
$x$ increases in $(\pi / 2, \pi)$

Discussion

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Top Algebra Educators
GH
Grace H.

Numerade Educator

Heather Z.

Oregon State University

Caleb E.

Baylor University

Michael J.

Idaho State University

Video Transcript

so we have. Why is equal to co sign two less so far things. What's the amplitude? So the amplitude of this will be to one, and the P AED would be to pie divided by two, which is equal to pi. So let's draw this graph So we have pi over four pi or two creep player four and pie and then de vie. Values would be limited between one and positive. One graph would look like this. So there's the craft. No, the X intercepts. There are two X intercepts which are X is equal to pi over four and excessive put through three pi work for and then the function is increasing or X values trading from pie or two to hi. So that's park now for Part B. All the answers would be the same, except for the amplitude. So everything else for Part B would be the same. So let's talk about part B part, he says. Why is he going to to co sign two X So, as I said, everything would be the same except for amplitude. And the amplitude now would be are too. So if you trod a graph now, it would still have pie or four hi or two. Did he power for? And Pie? But now, instead, off one. Are you going to say is that by managers Will very between negative two and positive. So the craft would now look like this So the X intercepts are still X is equal to pi over four x equal to three power for and it is increasing over detail from power to two pi.

Other Schools
Top Algebra Educators
GH
Grace H.

Numerade Educator

Heather Z.

Oregon State University

Caleb E.

Baylor University

Michael J.

Idaho State University