Results 1 to 12 of 12

Math Help - Help with a simple Sin proof

  1. #1
    Junior Member
    Joined
    Nov 2010
    From
    Colorado
    Posts
    42
    Thanks
    2

    Help with a simple Sin proof

    In any triangle sin(A + B)= sinC

    State true or false and explain why.

    The angles A,Band C are alpha, betta and gamma I just dont know how to put that in there so I used A,B andC.

    I tried to use an addition formula for sin and expand A+B to sines and cosines but I dont think that is right. The teacher wrote on the paper A+B=180-C which makes sense but there must be more than just that. If someone could get me going in the right direction I would appreciate it.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    A Plied Mathematician
    Joined
    Jun 2010
    From
    CT, USA
    Posts
    6,318
    Thanks
    4
    Awards
    2
    Could you try to show that sin(180-C) = sin(C)? If that's true, then you're pretty much done, right? If it's false, then the original claim is false.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Nov 2010
    From
    Colorado
    Posts
    42
    Thanks
    2
    Thanks for the quick reply. So the statement is true. At first I thought that angles A and B would have to be acute to add up to angle C but that does not seem to be the case. You can take the sine of any two angles and add them and as long as the third angle is the supplement. Why is this? Does it have to do with the unit circle and sine being positive from 0 to 180. Also they what you to explain why. How do I put it into words?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    A Plied Mathematician
    Joined
    Jun 2010
    From
    CT, USA
    Posts
    6,318
    Thanks
    4
    Awards
    2
    Well, show me your proof that sin(180-C) = sin(C). How would you go about showing this?
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Junior Member
    Joined
    Nov 2010
    From
    Colorado
    Posts
    42
    Thanks
    2
    Quote Originally Posted by Ackbeet View Post
    Well, show me your proof that sin(180-C) = sin(C). How would you go about showing this?
    I am not sure I understand what a proof is. Can you just put angles in for C and if it is true that is the proof? If so

    sin(180-90) = sin(90)
    sin(90) = sin(90)
    1 = 1

    or

    sin(180-30) = sin(30)
    sin(150) = sin(30)
    1/2 = 1/2

    maybe add for all angles from 0-180
    Follow Math Help Forum on Facebook and Google+

  6. #6
    A Plied Mathematician
    Joined
    Jun 2010
    From
    CT, USA
    Posts
    6,318
    Thanks
    4
    Awards
    2
    No, you cannot "prove by example", which is what you're proposing. You must prove in the abstract. Examples are useful in proofs only insofar as they make a proposition believable, but you can never prove by example (at least, not in this case. There is the proof method of "proof by cases", but that's only valid if you can enumerate every single example and prove all of them). You must show that sin(180-C) = sin(C) for all C. Considering that C can be any real number, you're going to be at it a very long time if you try to prove by example.

    Instead, I would recommend that you look at some trig identities, especially sum and difference identities. What ideas does that give you?
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Junior Member
    Joined
    Nov 2010
    From
    Colorado
    Posts
    42
    Thanks
    2
    sin(180-C) = sinC

    sin180cosC - cos180sinC = sinC

    0(cosC) - (-1)sinC = sinC

    -(-sinC) = sinC

    sinC = sinC

    Any better?
    Follow Math Help Forum on Facebook and Google+

  8. #8
    MHF Contributor
    Joined
    Mar 2010
    From
    Florida
    Posts
    3,093
    Thanks
    5
    Works for me.
    Follow Math Help Forum on Facebook and Google+

  9. #9
    A Plied Mathematician
    Joined
    Jun 2010
    From
    CT, USA
    Posts
    6,318
    Thanks
    4
    Awards
    2
    I agree with dwsmith. I'd say you're pretty much done. All you have to do, really, is preface your post # 7 with three lines:

    A + B + C = 180, which implies

    A + B = 180 - C, which implies

    sin(A+B) = sin (180-C),

    and then you insert your Post # 7 here. Got it?
    Follow Math Help Forum on Facebook and Google+

  10. #10
    Junior Member
    Joined
    Nov 2010
    From
    Colorado
    Posts
    42
    Thanks
    2
    Thanks Ackbeet that helped a lot. There are two others that I have to do. One I think I have figured out. I may have to create a thread on the other. Thanks again for the explanation on proofs.
    Follow Math Help Forum on Facebook and Google+

  11. #11
    MHF Contributor Also sprach Zarathustra's Avatar
    Joined
    Dec 2009
    From
    Russia
    Posts
    1,506
    Thanks
    1
    Quote Originally Posted by Ackbeet View Post
    I agree with dwsmith. I'd say you're pretty much done. All you have to do, really, is preface your post # 7 with three lines:

    A + B + C = 180, which implies

    A + B = 180 - C, which implies

    sin(A+B) = sin (180-C),

    and then you insert your Post # 7 here. Got it?
    One of my teachers at school was very pedant on every small things, especially about the degrees signs....

    So 180 is in degrees?
    Follow Math Help Forum on Facebook and Google+

  12. #12
    A Plied Mathematician
    Joined
    Jun 2010
    From
    CT, USA
    Posts
    6,318
    Thanks
    4
    Awards
    2
    AsZ is right. Don't write so that people can understand you. Write so they can't misunderstand you.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Simple proof
    Posted in the Statistics Forum
    Replies: 0
    Last Post: January 31st 2010, 05:17 PM
  2. Help with a simple proof
    Posted in the Calculus Forum
    Replies: 0
    Last Post: November 29th 2009, 12:43 PM
  3. simple proof. LHS = RHS
    Posted in the Calculus Forum
    Replies: 1
    Last Post: October 14th 2009, 04:55 PM
  4. Simple Proof
    Posted in the Algebra Forum
    Replies: 1
    Last Post: November 3rd 2008, 05:51 PM
  5. simple proof
    Posted in the Number Theory Forum
    Replies: 1
    Last Post: February 17th 2008, 05:15 PM

Search Tags


/mathhelpforum @mathhelpforum