#sin^2 x = 25/36# --> #sin x = +- 5/6#
Since x is in Quadrant 2, sin x is positive.
#sin x = 5/6#. Find cos x.
#cos^2 x = 1 - sin^2 x = 1 - 25/36 = 11/36#
#cos x = - sqrt11/6# (because x is in Q. 2).
#sin 2x = 2sin x.cos x = 2(5/6)(- sqrt11)/6 = - (5sqrt11)/18#
#cos 2x = 1 - 2sin^2 x = 1 - 50/36 = - 14/36 = - 7/18#
#tan 2x = sin 2x/(cos 2x) = ((-5sqrt11)/18)(- 18/7) =#
#tan 2x = (5sqrt11)/7#
Check by calculator.
#sin x = 5/6# --> #x = 123^@56# (Q. 3) --> #2x = 247^@12#
Calculator --> cos 247.12 = - 0. 39 --> tan 247.12 = 2.37
#cos 2x = - 7/18 = - 0.39#. Proved
#tan 2x = (5sqrt11)/7 = 2.37#. Proved.
