Aqa FP3 Polar Geometry(?)

I've been trying the paper below (Question 7). I've managed part a) but not part b).

The diagram looks as if the curve is symmetrical about the initial line and from there I would have done a bit of geometry to find where S was and so on. But I didn't know how to prove the curve was symmetrical so I decided to look at the answer. The first line says OS = 8 and it's only worth 1 mark so it must be obvious. But I don't know why.

Can anyone help please?

http://filestore.aqa.org.uk/subjects/AQA-MFP3-W-QP-JAN07.PDF

http://filestore.aqa.org.uk/subjects/AQA-MFP3-W-MS-JAN07.PDF

I've been trying the paper below (Question 7). I've managed part a) but not part b).

The diagram looks as if the curve is symmetrical about the initial line and from there I would have done a bit of geometry to find where S was and so on. But I didn't know how to prove the curve was symmetrical so I decided to look at the answer. The first line says OS = 8 and it's only worth 1 mark so it must be obvious. But I don't know why.

Can anyone help please?

http://filestore.aqa.org.uk/subjects/AQA-MFP3-W-QP-JAN07.PDF

http://filestore.aqa.org.uk/subjects/AQA-MFP3-W-MS-JAN07.PDF

What's the value of theta for OS? Look at the geometry.

To show symmetry about the intial line you want to show $r(\theta) = r(-\theta)$ treating r as a function of theta, which it is.