A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

anonymous

  • one year ago

Describe the graph of the cosine function.

  • This Question is Closed
  1. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    @ganeshie8

  2. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    @nincompoop @Preetha

  3. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    @campbell_st

  4. campbell_st
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    so do you know what the graph looks like...?

  5. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Hehe, not really

  6. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Let me check online

  7. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Pretty similar to the sine graph if you ask me...

  8. campbell_st
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    here 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

  9. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    ok, 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??

  10. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    @campbell_st

  11. campbell_st
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    so where does it cut the y-axis, are you working in radians or degrees..?

  12. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Degrees

  13. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    @campbell_st

  14. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Sorry to bother u, but I'm pretty lost...

  15. campbell_st
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    so so cos(90) =0 and cos(270) = 0 so the x- intercepts are at x = 90 and x = 270 then repeat every 180 degrees

  16. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Oooh, ok, so, as an answer, I put "starting at 90°, every 180°"?

  17. campbell_st
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    you could...

  18. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    would it be right?

  19. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    @ganeshie8 could u help me out pleease??

  20. SolomonZelman
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    There is a pattern to x-intercepts. For what values is cos(x)=0, the solutions to this are the x-intercepts. 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 y-intercept then, \(\large\color{black}{ \displaystyle x=90^\circ+180^\circ=270^\circ }\) is another x-intercept then, \(\large\color{black}{ \displaystyle x=90^\circ +180^\circ +180^\circ+.... }\) Each time you add 180º you get an x-intercept. 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 x-intercept. \(\large\color{black}{ \displaystyle x=90^\circ-180^\circ=-90^\circ }\) is an x-intercept \(\large\color{black}{ \displaystyle x=90^\circ-180^\circ-180^\circ=-270^\circ }\) \(\large\color{black}{ \displaystyle x=90^\circ -180^\circ -180^\circ-180^\circ-.... }\) 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 x-intercepts all go by the pattern \(\large\color{black}{ \displaystyle x=90^\circ -(180^\circ\times {\rm k});~~~\color{blue}{\rm \forall~~k\in{\bf Z}}}\)

  21. SolomonZelman
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    The blue notation here means "for all integer values of k"

  22. SolomonZelman
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    saying that k can be equal to ..... \(-5\), \(-4\), \(-3\), \(-2\), \(-1\), \(0\), \(1\), \(2\), \(3\), \(4\), \(5\), .....

  23. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Hehe, sorry @SolomonZelman , I'm not quite following... XD

  24. SolomonZelman
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Its alright....

  25. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    So what you're saying is that the x-intercepts are all multiples of 90?

  26. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    @SolomonZelman

  27. SolomonZelman
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    the x-intercepts start from 90º. and they are all the following: 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 NEGATIVE integer or 0. And ALSO, x-intercepts 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.

  28. SolomonZelman
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    this 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)

  29. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Is 180 an x-intercept? No right?

  30. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Aren't the x-intercepts the same as the sine and tangent graphs?

  31. SolomonZelman
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    no 180 is not, but 90 plus 180 (add or subtract 180 from 90 any number of times)

  32. SolomonZelman
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    lets look at it simple. (we are talking about the cos(x)=y graph) the x-intercepts are the values of x that make the y=0. these are as I posted: `~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~` the x-intercepts start from 90º. and they are all the following: 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 NEGATIVE integer or 0. And ALSO, x-intercepts 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. `~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~`

  33. SolomonZelman
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    so they are ....... -450º, -270º, -90º, 90º, 270º, 450º, .... (adding or subtracting 180 each time)

  34. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Yes, I understand now! So examples of intercepts would be 90, 270, 450, 630, 810, etc?

  35. SolomonZelman
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    yes, or you can subtract 180 from 90 many times 90 90-180=-90 -90-180=-270 -270-180=-450 and on....

  36. SolomonZelman
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    So, for this reason they can be all given using a pattern x = 90 + k•180 for all integers of k. (is this still unclear?)

  37. SolomonZelman
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    (all integers = ..... −5, −4, −3, −2, −1, 0, 1, 2, 3, 4, 5, ..... )

  38. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Great, and just to make sure, the rest of the cosine graph would be: y-intercept is 1, the domain are all real numbers and the range is -1≤x≤1

  39. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    right?

  40. SolomonZelman
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    the rest of the cosine graphs?

  41. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    No, I mean the rest of the characteristics of the cosine graph

  42. SolomonZelman
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    yes, yes. But provided they are not shifted sideways. they can have any angle of cx, such that y=cos(c•x)

  43. SolomonZelman
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    and the range will change if you shift it up/down

  44. SolomonZelman
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    so y=cos(x), has a range [-1,1] y-intercept 1

  45. SolomonZelman
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    but, y=cos(x+c) has a range of [-1,1] y-intercept 1-c

  46. SolomonZelman
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    and y=cos(x)+c has a range of [-1+c,1+c] y-intercept of 1

  47. SolomonZelman
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    this way y=cos(x+a)+b has a range of [-1+b,1+b] y-intercept 1-a

  48. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    I 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 x-intercepts are all odd multiples of 90?

  49. SolomonZelman
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Yes, negative or positive multiples of 90

  50. SolomonZelman
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    I mean negative or positive, odd multiples of 90

  51. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Thank you soooo much!!!

  52. SolomonZelman
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    in 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).

  53. SolomonZelman
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    this 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

  54. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Thanks!

  55. Not the answer you are looking for?
    Search for more explanations.

    • Attachments:

Ask your own question

Sign Up
Find more explanations on OpenStudy
Privacy Policy

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.