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Homework Help: Basic Trigonometric Limit

  1. Nov 12, 2008 #1
    Hi everyone,

    I would like to know, since the lim theta --> 0 (sine theta / theta) = 1, what is the limit theta --> 0 of cosine and tangent?

    Thank you very much in advance
  2. jcsd
  3. Nov 12, 2008 #2


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    Staff: Mentor

    What do you think they are? The cos(theta)/theta case seems pretty easy, right? And how is the sin(theta)/theta limit calculated? Can you use the same technique in the tan(theta)/theta case?
  4. Nov 12, 2008 #3


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    Science Advisor

    What do you mean by "limit of cosine and tangent"? If you mean those functions separately, they are continuous so the limit of cosine(theta) as theta goes to 0 is cos(0)= 1. The limit of tan(theta) as theta goes to 0 is tan(0)= 0.

    If you mean, as berkeman says, cos(theta)/theta, and tan(theta)/theta, all you need to know is that cos(theta)/theta has numerator close to 1 and denominator close to 0 for theta close to 0. For tan(theta)/theta, think tan(theta)= sin(theta)/cos(theta) so tan(theta)/theta= (sin(theta)/theta)/cos(theta).
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