Let’s consider the subspace of a vector space of all functions of a variable t.

Question

a) what are the coordinates of the function 3 sin t + 5 cos t = f(t) with respect to the basis {sin t, cost}?

b) Find coordinates with respect to base {cos t, sin t}

Answer 1

coordinates of f(t) = 3sint + 5cost with respect to the basis {sint, cost} are (3, 5)

coordinates of f(t) = 3sint + 5cost with respect to the basis {cost, sint} are (5, 3)