SOLUTION: Evaluate sin(v − w) if tan v = 3/4 v is in Quadrant III, sin w = − √(10)/10 and w is in Quadrant IV. sin(v − w) = Thank you

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Question 931504: Evaluate sin(v − w) if tan v = 3/4 v is in Quadrant III, sin w = − √(10)/10 and w is in Quadrant IV. sin(v − w) =

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Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
Evaluate sin(v − w) if tan v = 3/4 v is in Quadrant III, sin w = − √(10)/10 and w is in Quadrant IV.
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sinv=-3/5 (working with (3-4-5) reference right triangle in quadrant III where sin<0, cos<0.
cosv=-4/5
..
sinw=-√10/10
cosw=√(1-sin^2(w))=√(1-(1/√10)^2)=√(1-(1/10))=√(9/10)=3/√10=3√10/10
..
sin(v-w)=sinv*cosw-cosv*sinw=-3/5*3√10/10-(-4/5)*(-√10/10)
=-9√10/50-4√10/50=-13√10/50