Trig Identity Limit: Solving Trig Identities with Difficulty

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Homework Help Overview

The discussion revolves around evaluating the limit of a trigonometric expression as \( t \) approaches 0, specifically involving the function \( \frac{t^3}{\tan(2t)} \). The subject area includes trigonometric identities and limits.

Discussion Character

  • Mixed

Approaches and Questions Raised

  • Participants explore the use of L'Hôpital's rule as a potential method for solving the limit. Others suggest rewriting the tangent function in terms of sine and cosine to simplify the expression. There is also an attempt to manipulate the limit expression directly, leading to a calculation involving trigonometric functions.

Discussion Status

The discussion includes various attempts to evaluate the limit, with some participants providing guidance on possible methods. There is an acknowledgment of a calculation error in one of the posts, indicating an ongoing exploration of the problem.

Contextual Notes

Participants express difficulty with trigonometric identities, which may impact their approach to solving the limit. There is also a playful exchange regarding a calculation mistake, highlighting the informal nature of the discussion.

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Homework Statement



lim t3/tan32t
t->0

The Attempt at a Solution



I am stuck I have a lot of trouble with trig identities
 
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Do you know L'hôpital's rule? That might be the easiest way. If not, rewrite tan2t as sin2t/cos2t first. cos(2*0) won't cause a problem, but the t and sin2t will. See if you can get it to look like sin2t/t.
 
lim= 2*t*2*t*2*t*cos32t/2*sin2t*2*sin2t*2*sin2t\


so all the 2*t cancel the sin2t leaving cos32t/2*2*2 so limit=1/6

is this correct??
 
2*2*2=8, not 6. :wink:
 
haha you wow. :)
 

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