Question

(Linear Algebra)

Consider the vector space

H = Span {1, cos(t), cos2(t), cos3(t), cos4(t), cos5(t), cos6(t)}

Make a conjecture: what simple function could be used in place of f(t) = 1-8cos2(t)+ 8cos4(t) on the interval 0<t<2π

(use the graph of f(t) to find a much easier looking function that could be used in place of f(t)).

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Answer #1

Graph is below:

V1-S cos()+s(cos)) -3 0

Which coincides with the graph of cos(4r COS which we can use instead of 1 - 8 cos2 (x)8(cos(x)

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