SOLUTION: Find the exact value of the trigonometric function given that sin u = −8/17 and cos v = −5/13 (Both u and v are in Quadrant III.) cot(v − u)

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Question 921343: Find the exact value of the trigonometric function given that
sin u = −8/17
and
cos v = −5/13
(Both u and v are in Quadrant III.)
cot(v − u)
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
Find the exact value of the trigonometric function given that
sin u = −8/17
cos u =-√(1-sin^2 u)=-√(1-64/289)=-√(225/389)=-15/17
and
cos v = −5/13
sin v =-12/13 (working with a (5-12-13)right triangle)
(Both u and v are in Quadrant III.)
cot(v − u)
***
cos(v-u)=cos v*cos u+sin v*sin u
=(-5/13*-15/17)+(-12/13*-8/17)
=75/221+96/221=171/221
..
sin(v-u)=sin v*cos u-cos v*sin u
=(-12/13*-15/17)-(-5/13*-8/17)
=180/221-40/221
=140/221
..
cot(v-u)=cos/sin=171/140
Check:(w/calculator)
sin u=-8/17
u≈208.07˚..
cos v=-5/13
v≈247.38˚
v-u≈247.38-208.07≈39.31˚
tan(v-u)≈tan 39.31˚≈0.8188
cot(v-u)≈1/tan(v-u)≈1.2213
Exact value=171/140≈1.2214