If cot u 45 pi Solutioncot u 45 tan u 54 perpendicular 5

Solution

cot u = 4/5

tan u = 5/4

perpendicular = 5

base = 4

hypotenuse = sqrt 41

sin u = - 5 / sqrt 41

cos u = - 4 / sqrt 41

sin v = -5/13

perpendicular = 5

hypotenuse = 13

base = 12

cos v = 12/13

sin ( u + v ) = sin u cos v + cos u sin v = (-5/sqrt 41 )*(12/13) + ( -4/sqrt 41)(-5/13)

a) sin ( u+v ) = -60 / 13 sqrt 41 + 20 / 13 sqrt 41 = - 40 / 13 sqrt 41 = -40 sqrt 41 / 533

cos ( u+ v) = cos u cos v - sin u sin v = (- 4 / sqrt 41 )*(12/13) - ( - 5 / sqrt 41 )* (-5/13 )

b) cos ( u+v) = -48 / 13 sqrt 41 - 25 / 13 sqrt 41 = - 73 / 13 sqrt 41 = -73 sqrt 41 / 533

c) sin(u+v) and cos (u+v) are negative so (u+v) lies in 3rd quadrant