What is the exact value of the trig expression given that sinu= -3/5 and cosv=15/17?

Question

Tan(u+v)

Where sinu is 3pi/2<u<2pi

Where cosv is 0<u<pi/2

Answer 1

cosu = √1 - 9/25 = 4/5; tanu = sinu/cosu = (-3/5)/(4/5) = - 3/4;

sinv = √1 - 225/289 = 8/17; tanv = sinv/cosv = 8/15

tan(u + v) = (tanu + tanv)/(1 - tanutanv) = (- 3/4 + 8/15)/(1 + 3/4·8/15) = (-13/60)/(21/15) = - 13/84

Answer 2

based on those domains for u and v, u is in Quadrant 4 (negative sin, positive cos), and v is in Q1 (pos sin & cos).

cos u = sqrt(1 - (sin u)²) = sqrt (1 - 9/25) = sqrt (16/25) = 4/5

sin v = sqrt(1 - (15/17)²) = sqrt (1 - 225/289) = sqrt (64/289) = 8/17

tan u = sin u/cos u = -3/4

tan v = sin v/cos v = 8/15

tan (u+v) = (tan u + tan v)/(1 - tan u tan v)

= (-3/4 + 8/15)/(1 - (-24/60))

= (-45/60 + 32/60)/(60/60 + 24/60)

= (-13/60)/(84/60)

= -13/84