RATIONAL FUNCTION

Question

Express the following functions in the form f ◦ g where f is a rational function and g is a trigonometric function:

cos(t) a) u(t) = 1+cos(t) .

cos(t) b) w(t)= sin2(t).

Answer 1

I assume that the trig function listed before the problem is g(x)

a) f(t) = 1 + t

b) sin 2(t) = 2 sin(t) cos(t); as we are attempting to write this as a function of cos(t), we need to write sin in terms of cos sin(t) = sqrt(1 - cos^2(t))

Thus, f(t) = 2 t sqrt(1 - t^2)