(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

We just had a test in my calc 3 class, and I'm pretty sure my teacher has the wrong solution to one of the answers. The question is about finding the speed of a particle given a space curve function r(t) = (cos2t)i+ (3t - 1)j+ (sin2t)k.

2. Relevant equations

v(t) = (x',y',z')

|v(t)| = √(x' + y' + z')

3. The attempt at a solution

For velocity I get (-2sin2t)i+ (3)j+ (2cos2t)k. Now, for speed I put √(4sin^{2}2t + 4cos^{2}2t + 9) = 2(sin2t + cos2t) + 3. He marked it wrong saying that it can be reduced to √(4+9) = √(13). I was under the impression that the sin^{2}x + cos^{2}x = 1 identity only works if the variable stands alone in the function, as sin2t/cos2t calls for a double angle formula.

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# Homework Help: Finding speed from position equation

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