Question

How do you differentiate the following parametric equation: `x(t)=tcost, y(t)=tsint`?

Answer 1

`alpha'(t) = (x', y') (t)`

Explanation:

Differentiate `alpha = (x,y)` on `t`.

`x' = t'cost + t cos' t = 1 cos t + t (-sin t)`

`y' = t' sin t + t sin' t = 1 sin t + t (cos t)`

`alpha'(t) = ((cos t - t sin t), (sin t + t cos t))`