Also, For what values of θ do the maximum and minimum occur ?
I am assuming that you have graphed the two functions as required. I am GUESSING that the answers are to be given in radians.
Question a(iii) is one of those questions that are so absurdly easy that they confuse you. You say, "They must be asking something deeper than that."
$Let\ \theta_1\ be\ the\ value\ of\ \theta\ where\ cos(\theta )\ is\ maximum.\ So\ \theta_1 = what.$
$Let\ \theta_2\ be\ the\ value\ of\ \theta\ where\ sin(\theta )\ is\ maximum.\ So\ \theta_2 = what.$
The question is merely asking $\theta_2 - \theta_1 = what?$
The final question makes sense only if the overall question requires answers in radians. Otherwise the answer to what is the value of 50 degrees is 50 degrees.