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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 \((p,q).\)

 Sep 7, 2019
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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 )

 

check

 Sep 8, 2019

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