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anonymous
 one year ago
Describe the graph of the cosine function.
anonymous
 one year ago
Describe the graph of the cosine function.

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@nincompoop @Preetha

campbell_st
 one year ago
Best ResponseYou've already chosen the best response.0so do you know what the graph looks like...?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Pretty similar to the sine graph if you ask me...

campbell_st
 one year ago
Best ResponseYou've already chosen the best response.0here is a site that will graph it for you on the left side just enter y = cos(x) and you'll see the graph https://www.desmos.com/calculator

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ok, so now, just to make sure, the domain is all real numbers, the range is 1≤y≤1, the y intercept is 1, but what would the x intercepts be??

campbell_st
 one year ago
Best ResponseYou've already chosen the best response.0so where does it cut the yaxis, are you working in radians or degrees..?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Sorry to bother u, but I'm pretty lost...

campbell_st
 one year ago
Best ResponseYou've already chosen the best response.0so so cos(90) =0 and cos(270) = 0 so the x intercepts are at x = 90 and x = 270 then repeat every 180 degrees

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Oooh, ok, so, as an answer, I put "starting at 90°, every 180°"?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@ganeshie8 could u help me out pleease??

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1There is a pattern to xintercepts. For what values is cos(x)=0, the solutions to this are the xintercepts. For example at x=90 the cos(x) is 0 and so it is for x=270, for x=450 and on adding 180º each time.... \(\large\color{black}{ \displaystyle x=90^\circ }\) is your first yintercept then, \(\large\color{black}{ \displaystyle x=90^\circ+180^\circ=270^\circ }\) is another xintercept then, \(\large\color{black}{ \displaystyle x=90^\circ +180^\circ +180^\circ+.... }\) Each time you add 180º you get an xintercept. So, you can generate the pattern: \(\large\color{black}{ \displaystyle x=90^\circ +(180^\circ\times {\rm k})}\) (for all positive integer values of k, and for 0 as well) You can also go 180º , subtract 180º, to get the xintercept. \(\large\color{black}{ \displaystyle x=90^\circ180^\circ=90^\circ }\) is an xintercept \(\large\color{black}{ \displaystyle x=90^\circ180^\circ180^\circ=270^\circ }\) \(\large\color{black}{ \displaystyle x=90^\circ 180^\circ 180^\circ180^\circ.... }\) So, you can generate the pattern: \(\large\color{black}{ \displaystyle x=90^\circ (180^\circ\times {\rm k})}\) (for all negative integer values of k)  it follows that xintercepts all go by the pattern \(\large\color{black}{ \displaystyle x=90^\circ (180^\circ\times {\rm k});~~~\color{blue}{\rm \forall~~k\in{\bf Z}}}\)

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1The blue notation here means "for all integer values of k"

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1saying that k can be equal to ..... \(5\), \(4\), \(3\), \(2\), \(1\), \(0\), \(1\), \(2\), \(3\), \(4\), \(5\), .....

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Hehe, sorry @SolomonZelman , I'm not quite following... XD

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0So what you're saying is that the xintercepts are all multiples of 90?

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1the xintercepts start from 90º. and they are all the following: x=90180 x=90180180 x=90180180180 x=90180180180180 x=90180180180180180 x=90180180180180180..... and so on.... x=90+(k•180) where K IS NEGATIVE integer or 0. And ALSO, xintercepts are from 90 and +180 x=90+180 x=90+180+180 x=90+180+180+180 x=90+180+180+180+180 x=90+180+180+180+180+180 x=90+180+180+180+180+180...... and so on.... x=90+(k•180) where K IS POSITIVE integer or 0.

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1this why, you can generate a pattern with k (where k is both positive integers and negative integers and 0) and this pattern is: x=90+(k•180)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Is 180 an xintercept? No right?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Aren't the xintercepts the same as the sine and tangent graphs?

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1no 180 is not, but 90 plus 180 (add or subtract 180 from 90 any number of times)

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1lets look at it simple. (we are talking about the cos(x)=y graph) the xintercepts are the values of x that make the y=0. these are as I posted: `~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~` the xintercepts start from 90º. and they are all the following: x=90180 x=90180180 x=90180180180 x=90180180180180 x=90180180180180180 x=90180180180180180..... and so on.... x=90+(k•180) where K IS NEGATIVE integer or 0. And ALSO, xintercepts are from 90 and +180 x=90+180 x=90+180+180 x=90+180+180+180 x=90+180+180+180+180 x=90+180+180+180+180+180 x=90+180+180+180+180+180...... and so on.... x=90+(k•180) where K IS POSITIVE integer or 0. `~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~`

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1so they are ....... 450º, 270º, 90º, 90º, 270º, 450º, .... (adding or subtracting 180 each time)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Yes, I understand now! So examples of intercepts would be 90, 270, 450, 630, 810, etc?

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1yes, or you can subtract 180 from 90 many times 90 90180=90 90180=270 270180=450 and on....

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1So, for this reason they can be all given using a pattern x = 90 + k•180 for all integers of k. (is this still unclear?)

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1(all integers = ..... −5, −4, −3, −2, −1, 0, 1, 2, 3, 4, 5, ..... )

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Great, and just to make sure, the rest of the cosine graph would be: yintercept is 1, the domain are all real numbers and the range is 1≤x≤1

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1the rest of the cosine graphs?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0No, I mean the rest of the characteristics of the cosine graph

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1yes, yes. But provided they are not shifted sideways. they can have any angle of cx, such that y=cos(c•x)

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1and the range will change if you shift it up/down

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1so y=cos(x), has a range [1,1] yintercept 1

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1but, y=cos(x+c) has a range of [1,1] yintercept 1c

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1and y=cos(x)+c has a range of [1+c,1+c] yintercept of 1

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1this way y=cos(x+a)+b has a range of [1+b,1+b] yintercept 1a

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I just started learning the trig graphs, so I don't think the curves will shift. thanks anyways! One more thing, is it fair to say that the xintercepts are all odd multiples of 90?

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1Yes, negative or positive multiples of 90

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1I mean negative or positive, odd multiples of 90

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Thank you soooo much!!!

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1in this case of y=cos(x), which is not the case if you shift the graph sideways such that y=cos(x+b), and which is not [neccessarily, but for most values in fact not] the case if you multiply the angle or the function times a scale factor, such that: y=cos(bx), or y=bcos(x).

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1this is just graph shifts..... the rule you can get in a book or online..... my PC is about to resart because I am scanning and updating. cu
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