The curve \(y = \sin x\) cuts the line whose equation is \(y = \sin 70^\circ\) into segments having the successive ratios \(\dots p : q : p : q \dots\) with \(p < q.\) Compute the ordered pair of relatively prime positive integers \((p,q).\)
Find the intersection of y=sin 70 and y=sinx
x=70+360n or x= 180-70+360n where n is an integer.
x= 70, 110, 360+70, 110+360, ......
p=110-70=40 q= 360+70-110 = 320
(p,q) = ( 40. 320 )