Question #bab8a

1 Answer
Aug 16, 2016

If phi is the angle of 3rd quadrant then

cosphi->-ve and sinphi->-ve

Now sin2phi=2sinphicosphi

=-2sqrt(1-cos^2phi)*cosphi

=-2sqrt(1-(-15/17)^2)*(-15/17)

=+2sqrt(17^2-15^2)/17*xx15/17

=(2*8*15)/17^2=240/289

2phi=sin^-1(240/289)
~~56.14^@color(red)(->2phi" is in the 1st quadrant")

Again

cosphi=-15/17

phi=cos^-1(-15/17)=360-151.93=208.07
color(red)(("As "phi" is in the 3rd quadrant"))

:.2phi=416.14=360+56 .14

So 2phi is the angle of 1st quadrant.