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WHAT IS the total length of the curve y = 4 sin (theta)

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Since the domain is all reals, the curve has no finite length.
However, in rectangular coordinates, one arch of the curve has length
a = ∫[0,π] √(1 + 16cos^2θ) dθ = 8.81
not an elementary integral

In polar coordinates, since it is just a circle of radius 1/2, C = π

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