Question

Consider the graph of the cosine function shown below.

Answer 1

https://www.connexus.com/content/media/666994-2212012-111042-AM-103506273.png


a. find the period and amplitude of the cosine function
b. at what values of \[\theta \]for 0 \[\le \] 1\[\theta \]\[\le \]2pi do the maximum value(s), minimum value(s) and zeros occur?

Answer 2

\[0\le \theta \le2\pi \]

Answer 3

When I clicked your link I got "Access Denied, you must log in first". Any other options for you to post it?

Answer 4

Ok, the period is how much of the graph one "revolution" of the curve covers. Like, in this case, one time up from the x axis down through the x axis, down to its lowest point and then back up to meet the x axis, but not through it, in other words, this:
The amplitude is how high and low it goes, but it is the positive range of the function, or how high up the y axis it goes. Your function goes up how high on the y axis? 2, right? So that's the amplitude. Amplitude can NEVER be a negative number. Now for the period. The graph is divided up into 4ths: \[\frac{ \pi }{ 4 },\frac{ \pi }{ 2 },\frac{ 3\pi }{ 4 },\pi \]The first place the graph goes through the x axis is halfway between pi over 4 and pi over 2, which is pi over 8, or \[\frac{ \pi }{ 8 }\] Then it goes down to -2 at pi over 4, then it comes back up through the x axis halfway between pi over 4 and pi over 2, then goes up to its peak (2) at pi over 2, then comes back down to complete one cycle at 5pi over 8. So the whole period occurs between \[\frac{ \pi }{ 8 }-->\frac{ 5\pi }{ 8 }\]The difference between these is \[\frac{ 5\pi }{ 8 }-\frac{ \pi }{ 8 }=\frac{ 4\pi }{ 8 }=\frac{ \pi }{ 2 }\]So pi over 2 is the period. I'm not sure what the rest of your question is looking for, so please let me know. The way you have entered it is confusing!

Answer 5

ill re-enter it for you. for some reason it became scattered.

Answer 6

b. at what values of \[\theta for 0\le \theta \le 2\pi \]