document.write( "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) ? \n" ); document.write( "

Algebra.Com's Answer #500678 by stanbon(75887) $\"\"$ $\"About$

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when sin x= -8/17 and x lies in Quadrant III where x < 0 and y < 0
\n" ); document.write( "Find cos(x)::::::
\n" ); document.write( "sin = y/r, so y = -8 , r = 17
\n" ); document.write( "Then x = -sqrt[17^2-8^2] = -sqrt[225) = -15
\n" ); document.write( "So cos = x/r = -15/17
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\n" ); document.write( "and cos y= -4/5 and y lies in Quadrant II
\n" ); document.write( "Find sin(y)::::::
\n" ); document.write( "y = sqrt[25-16] = 3
\n" ); document.write( "So sin = y/r = 3/5
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\n" ); document.write( "What is cos(x-y) ?
\n" ); document.write( "------
\n" ); document.write( "Formula: cos(x-y) = cos(x)cos(y)+sin(x)sin(y)
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\n" ); document.write( "cos(x-y) = (-15/17)(-4/5) + (-8/17)(3/5)
\n" ); document.write( "= (0.7059)+(-0.2824) = 0.4235
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\n" ); document.write( "Cheers,
\n" ); document.write( "Stan H.
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