Deriving tangential and normal acceleration components

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Markel
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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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  • Handwritten diagram of a circle with points P and P' on it, velocity vectors v and v' drawn tangent, and a triangle with vertex O, angle Δθ, and point S at a right angle, with equations MS = v' cos Δθ − v and SQ = v' sin Δθ.
    physics 1.jpg
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Last edited:
oops. figured this out. Sorry, this was really silly.