Trigonometric Expression Problem ''Express $sin(4α)$ as a function of $α $ only''?
What does it mean? how can one express a trigonometric function using only angles? 

It means that you have to express $sin(4\alpha)$ as a function of trigonometric functions with only $\alpha$ as argument. Use the following formulae:
$$sin(2\alpha)=2sin(\alpha)cos(\alpha)$$
$$cos(2\alpha)=cos^2(\alpha)-sin^2(\alpha)$$
