Yazomi
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What did I do wrong in this question
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dew1223345
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don't combine differentiate both functions separately by dy/dt and dx/dt then divide the dy/dt by dx/dt to get dy/dx in the form of t
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davros
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(Original post by Yazomi)
What did I do wrong in this question
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Two things:

Firstly, you shouldn't be finding y in terms of x, you should be using the standard parametric formula dy/dx = (dy/dt) / (dx/dt).

Secondly you have created a problem for yourself - because t can take on negative values and y = 3sin t, it is possible for y to be negative. But when you write y = (something)^(1/2) you are choosing the positive value of the square root as that is the convention for both the square root symbol and the power 1/2 (otherwise you wouldn't have a valid function). Therefore you need to be really careful when manipulating parametric equations.

(Note: you could write x in terms of y^2 and use implicit differentiation if you have covered that. That would eliminate the problem caused by taking square roots.)
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