P is in the Quadrant II.
We have: #angle t = (pi/2 + angle a).#
Angle a is defined by #tan a = 2/3# --> #sin a = 2/sqrt(4 + 9) = 2/sqrt13# -->
#cos^2 a = 1 - sin^2 a = 1 - 4/13 = 9/13# --> #cos a = 3/sqrt13#.
Find the trig functions of t.
#sin t = sin (a + pi/2) = cos a = 3/sqrt13#
#cos t = cos (pi/2 + a) = - sin a = - 2/sqrt13#
#sin 2t = 2sin t.cos t = - (2/sqrt13)(3/sqrt13) = - 6/13#
#cos^2 2t = 1 - sin^2 t = 1 - 36/169 = 133/169#
#cos 2t = - sqrt133/13#. (2t is in Quadrant III)
sin (t - 150) = sin t.cos 150 - sin 150.cos t.
#= - (3/sqrt13)(-sqrt3/2) - (1/2)(-2/sqrt13) =#
#= - ((3sqrt3)/(2sqrt13)) + (2/(2sqrt13)) = (2 - 3sqrt3)/(2sqrt13)#
cos (225 - t) = cos 225.cos t + sin 225.sin t =
#cos 225 = -cos 45 = -sqrt2/2# ; and #sin 225 = -sin 45 = -sqrt2/2#
