Quantcast

Got Homework?

Connect with other students for help. It's a free community.

  • across
    MIT Grad Student
    Online now
  • laura*
    Helped 1,000 students
    Online now
  • Hero
    College Math Guru
    Online now

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

eigenschmeigen Group Title

is there a method for proving the following without calculus or arguing by a diagram?

  • 2 years ago
  • 2 years ago

  • This Question is Closed
  1. eigenschmeigen Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    \[\forall x \ge 0 \text{ }\sin(x) \le x \]

    • 2 years ago
  2. eigenschmeigen Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    @Callisto

    • 2 years ago
  3. hba Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    Actually calculus is a very powerful tool to solve problems.So Most of the problems can be solved my Calculus,Therfore,they maybe other ways to solve questions without the use of calculus.

    • 2 years ago
  4. amistre64 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    yelling, shouting, and just being overall obnoxius tend to be used by kids today to prove their point :)

    • 2 years ago
  5. hba Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    lol ^

    • 2 years ago
  6. Callisto Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    I don't know if this works lol -1<sinx <1 -x < xsinx < x xsinx < x <- see this?!

    • 2 years ago
  7. eigenschmeigen Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    that works for 1=<x but i dont think it helps particularly for the harder case 0=<x=<1

    • 2 years ago
  8. mahmit2012 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    |dw:1353765596912:dw|

    • 2 years ago
  9. eigenschmeigen Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    yeah see that's what i meant by arguing from a diagram

    • 2 years ago
  10. eigenschmeigen Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    maybe using the cosine rule we can convert the diagram proof into something more formal

    • 2 years ago
  11. amistre64 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    arent most things proved by being vague and nondescript? or is it just my number theory text that does that?

    • 2 years ago
  12. eigenschmeigen Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    haha

    • 2 years ago
  13. mahmit2012 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    |dw:1353765811446:dw|

    • 2 years ago
  14. eigenschmeigen Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    hmm are you using the area of a sector there? doesn't that require calculus?

    • 2 years ago
  15. mahmit2012 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    Yes it doesn't. It just uses compare between to area. And first one compare two line and curve.

    • 2 years ago
  16. asnaseer Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    |dw:1353766410319:dw|

    • 2 years ago
  17. asnaseer Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    from that diagram you can see that: sin(x) = b/c

    • 2 years ago
  18. asnaseer Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    also, from arc length, we know: cx = s (assuming x is measured in radians)

    • 2 years ago
  19. asnaseer Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    so x = s/c

    • 2 years ago
  20. asnaseer Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    but s > d

    • 2 years ago
  21. asnaseer Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    and d > b

    • 2 years ago
  22. asnaseer Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    therefore sin(x) <= x

    • 2 years ago
  23. asnaseer Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    I am starting the proof off from the basic definition of what sin(x) represents. so you need a diagram.

    • 2 years ago
  24. asnaseer Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    @eigenschmeigen - what "methods" are you looking for if no diagrams can be used?

    • 2 years ago
  25. hba Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    lol

    • 2 years ago
  26. hba Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    He doesn't want geometry or Calculus.

    • 2 years ago
  27. UnkleRhaukus Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    the sine of an angle in a triangle (with the opposite side equal to one,) is the length of the hypotenuse, the hypotenuse is the longest side of a triangle the angle \(x\) is a measure of the arc, the arc is longer than the opposite side

    • 2 years ago
  28. eigenschmeigen Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    my situation is that im using this fact as part of a solution to a problem on my analysis sheet, last time i thought i could state it without giveing a proof (at the top of the sheet it said we may assume basic properties of trig functions) in the course we have only defined sinx in terms of its power series. should i just show that for 0<x<1 the power series converges to a limit less than x?

    • 2 years ago
  29. eigenschmeigen Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    when i stated it without proof my tutor wrote "why?" next to it which means i should have given some form of proof

    • 2 years ago
  30. asnaseer Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    aren't you contradicting yourself here - the power series is derived using calculus and you stated "no calculus allowed"?

    • 2 years ago
  31. eigenschmeigen Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    no, in our course we are _defining_ the functions sin, cos, e^x as their power series, we are not deriving them through the maclauren.

    • 2 years ago
  32. mahmit2012 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    But power series related to advance calcules!

    • 2 years ago
  33. mahmit2012 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    x-sinx=x3/3!-x5/5!+-...>0 for all x>0

    • 2 years ago
  34. eigenschmeigen Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    http://www.maths.ox.ac.uk/system/files/coursematerial/2012/2644/22/12MT-AnalysisI-extsyn13.pdf

    • 2 years ago
  35. eigenschmeigen Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    of course i know its related. the way we are doing it (which is perfectly valid) is by defining the functions as the power series and deriving properties from there.

    • 2 years ago
  36. mahmit2012 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    The link you have already suggested was about complex function, and we know there is no comparing in complex number. And also sinZ is not bounded.

    • 2 years ago
  37. eigenschmeigen Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    its given as sinz but thats the general case of sinx...

    • 2 years ago
  38. eigenschmeigen Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    im fed up. dont worry ill figure it out

    • 2 years ago
  39. CliffSedge Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    @UnkleRhaukus , did you mean to say, "the sine of an angle in a triangle (with the *hypotenuse* equal to one,) is the length of the *opposite side*, . . . " ?

    • 2 years ago
  40. UnkleRhaukus Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    whoops,and yeah @CliffSedge , its kinda hard when you dont draw it

    • 2 years ago
  41. CliffSedge Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    Yeah, why wouldn't someone want a diagram?

    • 2 years ago
  42. eigenschmeigen Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    you cant argue from a diagram in formal mathematics. i cant exactly draw a diagram and hand it in to my analysis tutor

    • 2 years ago
    • Attachments:

See more questions >>>

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.