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 √(4sin22t + 4cos22t + 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 sin2x + cos2x = 1 identity only works if the variable stands alone in the function, as sin2t/cos2t calls for a double angle formula.