Exact Value of Trigonometry Expression

Question

Find the exact value of the trigonometric expression given that sin(u) = − 3/5

,

 where 3𝜋/2 < u < 2𝜋,

and cos(v) = 15/17

,

 where 0 < v < 𝜋/2.

tan(u + v

Answer 1

Hard to see how to get an "exact" solution, but

u=-36.87 = 323,1 degrees = 1.8 pi radians

v = 28.36 degrees = 0.16 pi radians

tan(u+v) = -0.15 = nearly zero, as u+v is close to 360 degrees or 2 pi

However rounding errors may have caused that difference.

It's possible that the way to solve this for an exact solution is use some trigonometric identities.and maybe

that leads to tan(u+v) = 0. Just a guess.

the above calculations are just from a calculator with trig functions.