The vector space H = Span {1, cos2 t, cos4 t, cos6 t} contains at least two interesting functions that will be used in a later exercise:

Study the graph of f for 0 ( t ( 2(, and guess a simple formula for f(t). Verify your conjecture by graphing the dif between 1 C f(t) and your formula for f(t). (Hopefully, you will see the constant function 1.)
Repeat Exercise 37 for the function
f(t) = 3 sin t - 4 sin3 t
g(t) = 1 - 8 sni2 t + 8 sin4 t
h(t) = 5sin t - 20 sin3 t + 16 sin5 t

f(t ) = 1-8 + 8 cos g) 18 cos21 48 costt 32 cos t cos- t