Question 830487: when sin x= -8/17 and x lies in Quadrant III and cos y= -4/5 and y lies in Quadrant II, what is cos(x-y) ?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! when sin x= -8/17 and x lies in Quadrant III where x < 0 and y < 0
Find cos(x)::::::
sin = y/r, so y = -8 , r = 17
Then x = -sqrt[17^2-8^2] = -sqrt[225) = -15
So cos = x/r = -15/17
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and cos y= -4/5 and y lies in Quadrant II
Find sin(y)::::::
y = sqrt[25-16] = 3
So sin = y/r = 3/5
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What is cos(x-y) ?
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Formula: cos(x-y) = cos(x)cos(y)+sin(x)sin(y)
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cos(x-y) = (-15/17)(-4/5) + (-8/17)(3/5)
= (0.7059)+(-0.2824) = 0.4235
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Cheers,
Stan H.
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