Oxford Admissions Question - Sum of Sine Functions

This is a question from the Oxford University Mathematics Admissions Test 2019.

[gdmathguy]

So 3 crucial things to know:
1. sin(0)=0, therefore the infinite sum of sines will also be 0 at 0 which will repeat every 180°
2. sin(90°)=1, therefore the infinite summation will include an infinities at 90° repeated at each 180°
3. Since all powers of sin are even, that means that all values we get from this function will be even too.

So lets rule out stuff:
With 3 we can rule out e
With 2 we can rule out b and c and
With 1 we can rule out a making

D the right solution

[asparkdeity]

Just plug in key values, suppose the desired function is S(x);

sin(0) = 0
sin(90) = 1
sin(180) = 0

Thus:
S(0) = 0
S(90) is divergent
S(180) = 0

The only graph where these 3 conditions are satisfied is D