document.write( "Question 823644: Let sin s = (-1/4), with s in quadrant 4 and cos t = (-4/5), with t in quadrant 2.
\n" ); document.write( "Find sin(s+t) and explain. \n" ); document.write( "

Algebra.Com's Answer #495660 by stanbon(75887) $\"\"$ $\"About$

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Let sin(s) = (-1/4), with s in quadrant 4
\n" ); document.write( "and cos(t) = (-4/5), with t in quadrant 2.
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\n" ); document.write( "Find cos(s)::
\n" ); document.write( "Since sin(s) = y/r = -1/4, y = -1 and r = 4
\n" ); document.write( "Therefore x = sqrt[4^2-1^2] = sqrt(15)
\n" ); document.write( "And cos(s) = x/r = sqrt(15)/4
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\n" ); document.write( "Find sin(t)::
\n" ); document.write( "Since cos(t) = x/r = -4/5, x = -4 and r = 5
\n" ); document.write( "Therefore y = sqrt[5^2-4^2] = 3
\n" ); document.write( "So sin(t) = y/r = 3/5
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\n" ); document.write( "Find sin(s+t) = sin(s)cos(t)+cos(s)sin(t)
\n" ); document.write( "-----
\n" ); document.write( "= (-1/4)(-4/5)+(sqrt(15)/4)(3/5)
\n" ); document.write( "------
\n" ); document.write( "= (1/5)+(3sqrt(15)/20)
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\n" ); document.write( "= [4+3sqrt(15)]/20
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\n" ); document.write( "= 0.7809
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\n" ); document.write( "Cheers,
\n" ); document.write( "Stan H.
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