Find the exact value of the trigonometric expression given t
Find the exact value of the trigonometric expression given that sin u = 3/5 and cos v = 24/25. (Both u and v are in Quadrant III.) csc(u - v)
Solution
sin u =-3/5
cos u = - 4/5
cos v = -24/25
sin v = -7/25
csc ( u-v) = 1 / sin (u-v)
sin (u-v) = sin u cos v - cos u sin v
plugging the values in the formula
sin (u-v) = (-3/5) (-24/25) - (-4/5)(-7/25)
sin (u-v) = 72/125 - 28/125 = 44/125
therefore,
csc (u-v) = 1/ sin (u-v) = 125/44
