Suppose that cos (t) = 5/13, where t is the fourth quadrant. find sin (2t)

Given that cos (t) = 5/13

t is in fourth quadrant, so sint0

So sint = - sqrt (1-cos^2 (t)) = - sqrt (1-25/169) = - sqrt ((169-25) / 169) = - 12/13

Sin (2t) = 2sin (t) cos (t) = 2*-12/13 * 5/13 = - 120/169