given that sec(a)=t+1/t-1 for some angle a, t belongs to any real numbers, if a is in the fourth quadrant, determine the exact value for sin a.

Answer 1

sec(a) = 1/cos(a) = (t+1)/(t-1)

cos(a) = (t-1)/(t+1) = adjacent side/hypotenuse where hypotenuse>0, adjacent side>0

sin(a) = opposite side/hypotenuse, with opposite side<0

cos(a)>0, sin(a)<0 in quandrant IV

opposite side = -sqr(hypotenuse^2-adjacent side ^2) =-sqr((t+1)^2 - (t-1)^2)

= -sqr(t^2+2t+1 - t^2 +2t -1) = -sqr(4t) = -2sqrt

sin(a) = -2sqrt/(t+1) = minus two times the square root of t divided by (t+1)