If sin(u)=5/13, pi/2<u<pi and tan(v)=7/24, pi<v<3pi/2, find tan(u+v). Round answer to the nearest thousandth.

Answer 1

just need to use the tangent addition formula Tan(u+v) = tan u + tan v / 1- Tan(u)Tan(v)

Since sin u (opposite/hypotenuse) = 5/13 the third or adjacent side = 12 so tan u = 5/12

So tan(u+v)= (5/12) +(7/24) / 1 -(5/12)(7/24) =

17/24 / 1-35/288=

204/288 / 253/288= 204/253