Find the exact value of the trigonometric function given that sin u = -5/13 and cos v = -20/29. (Both u and v are in Quadrant III.) tan(u − v)

Tan(u–v) = –304/690

Step-by-step explanation:

Putting in mind that sin(theta) and cos(theta) are both negative in the third quadrant, we can find sin(v) and cos(u).

sin(u) = – 5/13 we have opp = 5 and hyp = 13, we make use of Pythagoras theorem to find adj.

Adj = √(13² – 5²) = √(169 – 25) = √144 = 12

cos(u) = – 12/13, therefore tan(u) = 5/12.

cos(v) = –20/29 we have adj = 20 and hyp = 29, we make use of Pythagoras theorem to find opp.

OPP = √(29² – 20²) = √(841 – 400) = √441 = 21

sin(v) = – 21/29, therefore tan(v) =21/20.

tan(u-v) = [tan(u) - tan(v)]/[1 + tan(u)xtan(v)] = [(5/12) - (21/20)]/[1 + (5/12)X(21/20)] = (–19/30)÷(1+7/16) = (–19/30)÷(23/16) =

–304/690

step-by-step explanation: