`cos(u - v)` Find the exact value of the trigonometric expression given that sin(u) = 5/13 and cos(v) = -3/5 (both u and v are in quadrant II.)

Given `sin(u)=5/13,cos(v)=-3/5`

Angles u and v are in quadrant 2.

A right triangle can be drawn in quadrant 2. Since `sin(u)=5/13` you know that the side opposite of angle u is 5 and the hypotenuse is 13. Using the pythagorean theorem the third side of the triangle is 12.

A right triangle can be drawn in quadrant 2 since `cos(v)=-3/5` you know

that the side adjacent to angle v is 3 and the hypotenuse is 5. Using the pythagorean theorem the third side of the triangle is 4.

`cos(u-v)=cos(u)cos(v)+sin(u)sin(v)`

`cos(u-v)=(-12/13)(-3/5)+(5/13)(4/5)=36/65+20/65=56/65`