Sample Problem

Given that sin u=-7/16 and cos v=-5/8, find the exact value of cot (v-u).

Both u and v are in Quadrant III.


If sin u=-7/16, cos u=±√(207/256)=-√207/16 (because we know u is in Quadrant III)

tan u=sin u/cos u=7/√207

If cos v=-5/8, sin v=±√(39/64)=-√39/8 (because we know v is in Quadrant IV)

tan v=sin v/cos v=5/√39

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