both u and v are in quadrant III
from sin u = -8/17 ----> y = -8 , r = 17
x^2 + 64 = 289 --> x = -15 in quad III
cosu = -15/17
from cos v = 12/13 ---> x = 12, r = 13
y = ± 5
if v is in I, sinv = 5/13 , cosv = 12/13
if v in in IV , sinv = -5/13, cosv = 12/13
cos(u+v) = cosu cosv - sinu sinv
if v is in I :
= (-15/17)(12/13) - (-8/17)(5/13) = -140/221
if v is in IV
= (-15/17)(12/13) - (-8/17)(-5/13) = -220/221
Let sin u=-8/17 and cos v= 12/13, with pie<u<3pie/2. Find the exact value of cos(u+v)
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