Question

Let C be parametrized by x = 10 sin^2(t) and y = 10 sin (t) cos (t) for 0 ≤ t ≤ π/2

Find the length L of C.

Answer 1

cos(2t) = 5 - x
sint(2t) = y

Hence, this is a circle. Try to find the length of arc C (using mental maths)

Answer 2

How'd you get those two exactly?

Answer 3

Use trigonometry to reduce the powers ; see formulas
\[\cos(2t) = 1 - 2\sin^2(t)\]
\[\sin(2t) = 2\sin(t) \cos(t)\]