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Math Help - LIMITS and CONTINUITY !!!!

  1. #1
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    LIMITS and CONTINUITY !!!!

    prove that cosine is a continuous function!!

    how do you prove that it is continuous using limit laws?
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  2. #2
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    Re: LIMITS and CONTINUITY !!!!

    In this thread you are supposed to prove that sine is continuous. Cosine can be expressed through sine. Or use the same method as for sine.
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    Re: LIMITS and CONTINUITY !!!!

    Quote Originally Posted by pnfuller View Post
    prove that cosine is a continuous function!!
    how do you prove that it is continuous using limit laws?
    Show that {\lim _{h \to 0}}\cos \left( {x + h} \right) = \cos (x)
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    Re: LIMITS and CONTINUITY !!!!

    and how do you do that?
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  5. #5
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    Re: LIMITS and CONTINUITY !!!!

    Prove that sin(x) and cos(x) are continuous at x= 0, first. Then use the fact that cos(x+y)= cos(x)cos(y)- sin(x)sin(y). How you prove that sin(x) and cos(x) are continuous at x= 0 depends on precisely how you have defined sine and cosine.
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