Also, For what values of θ do the maximum and minimum occur ?
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.