Precalculus, Chapter 5, 5.4, Section 5.4, Problem 47

Given sin(u)=-7/25,cos(v)=-4/5
Angles u and v are in quadrant 3.
A right triangle can be drawn in quadrant 3. Since sin(u)=-7/25 we know that the side opposite angle u is 7 and the hypotenuse is 25. Using the pythagorean theorem the third side of the triangle is 24.
A right triangle can be drawn in quadrant 3. Since cos(v)=-4/5 we know that the side adjacent to angle v is 4 and the hypotenuse is 5. Using the pythagorean theorem the third side of the triangle is 3.
cos(u+v)=cos(u)cos(v)-sin(u)sin(v)
cos(u+v)=(-24/25)(-4/5)-(-7/25)(-3/5)=(96/125)-(21/25)=75/125=3/5