Tangential & normal acceleration derivations

AI Thread Summary
The discussion focuses on the derivation of tangential acceleration in physics, highlighting confusion over the use of trigonometric functions in a triangle related to velocity components. The original poster questions the equation used to find the opposite side, suggesting it should involve tangent rather than sine. They realize their mistake and clarify that the correct relationship involves sine as it pertains to the triangle's sides. The conversation emphasizes the importance of understanding trigonometric relationships in physics derivations. Ultimately, the poster resolves their confusion and acknowledges the oversight.
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I'm trying to understand how my book derives the tangential accelration. I drew a picture because it's kind of confusing to explain.

From the triangle we get the tangential and normal components of the velocity.

What my problem is (and I think, and hope, it's something simple that I just can't see) that in the second equation where they find SQ.

They times they take adjacent x sin(angle) = oposite.

but isn't sin = oposite/hypoteneuse ??

shouldn't the formula be adjacent x tan(angle) = opposite = SQ ?
 

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oops. figured this out. Sorry, this was really silly.
 
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