# actual evaluation – Number of zeros of a sine polynomial Answer

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actual evaluation – Number of zeros of a sine polynomial

Let $$(a_i)_{i=1}^{n}$$ breathe non-negative, then what number of actual zeros does the sine polynomial
$$p(theta) := a_1sin(theta) + a_2sin(2theta) + cdots + a_nsin(ntheta), quad theta in [0,2pi)$$
have?

Furthermore:

• Clearly $$theta = 0,pi$$ are zeros of $$p$$. What standards for $$(a_n)$$ live for these to breathe the solely zeros.

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