b) is correct but you probably need to justify your answer better. After all you can't usually just add and subtract lengths like this.

c) Since the circle does not contain the origin, and does not pass through the x axis the minimum and maximum values of the argument occur at the points where lines through the origin are tangent to the circle. Let the centre of the circle be C and the point of tangency be P. angle OPC is a right angle. You know the length of OC and CP, so you have a right angled triangle for which CP/OC is the sine of angle POC. Given that you already know the argument of C you can then easily find the arguments of the two points of tangency. So you can find the answer without actually finding the coordinates of the two tangent points!