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trignometric equations help

Quote:

(b) The diagram shows part of the curve with equation *y*=cos(px−*q*)° , where *p* and *q* are positive constants and *q*<180. The curve cuts the *x*-axis at points *A*, *B* and *C*, as shown.

Given that the coordinates of *A* and *B* are (100, 0) and (220, 0) respectively:

(i) Write down the coordinates of *C*.

(ii) Find the value of *p* and the value of *q*.

I have guessed that the coordinates of C is (340,0), which is correct, but is there any 'formal' way of working out the coordinates of C?

Also can someone show me how to work out the vales of p and q?

thank you.