Find two fourier expansions for the function h(x) = sin(x). In one expansion, all the sine...

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Find two fourier expansions for the function h(x) = sin(x). In one expansion, all the sine terms should have zero as their coefficient. In the other expansion, all the cosine terms should have zero as their coefficient. Hint: Restrict h(x) to two different domains. Keep in mind that it suffices to know the value of sin(x) on [0,] in order extrapolate all other values of sin(x). Find two fourier expansions for the function h(x) = sin(x). In one expansion, all the sine terms should have zero as their coefficient. In the other expansion, all the cosine terms should have zero as their coefficient. Hint: Restrict h(x) to two different domains. Keep in mind that it suffices to know the value of sin(x) on [0,] in order extrapolate all other values of sin(x).