document.write( "Question 921343: Find the exact value of the trigonometric function given that
\n" ); document.write( "sin u = −8/17
\n" ); document.write( " and
\n" ); document.write( "cos v = −5/13\r
\n" ); document.write( "\n" ); document.write( " (Both u and v are in Quadrant III.)
\n" ); document.write( "cot(v − u) \n" ); document.write( "
Algebra.Com's Answer #558958 by lwsshak3(11628)\"\" \"About 
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Find the exact value of the trigonometric function given that
\n" ); document.write( "sin u = −8/17
\n" ); document.write( "cos u =-√(1-sin^2 u)=-√(1-64/289)=-√(225/389)=-15/17
\n" ); document.write( "and
\n" ); document.write( "cos v = −5/13
\n" ); document.write( "sin v =-12/13 (working with a (5-12-13)right triangle)
\n" ); document.write( "(Both u and v are in Quadrant III.)
\n" ); document.write( "cot(v − u)
\n" ); document.write( "***
\n" ); document.write( "cos(v-u)=cos v*cos u+sin v*sin u
\n" ); document.write( "=(-5/13*-15/17)+(-12/13*-8/17)
\n" ); document.write( "=75/221+96/221=171/221
\n" ); document.write( "..
\n" ); document.write( "sin(v-u)=sin v*cos u-cos v*sin u
\n" ); document.write( "=(-12/13*-15/17)-(-5/13*-8/17)
\n" ); document.write( "=180/221-40/221
\n" ); document.write( "=140/221
\n" ); document.write( "..
\n" ); document.write( "cot(v-u)=cos/sin=171/140\r
\n" ); document.write( "\n" ); document.write( "Check:(w/calculator)
\n" ); document.write( "sin u=-8/17
\n" ); document.write( "u≈208.07˚..
\n" ); document.write( "cos v=-5/13
\n" ); document.write( "v≈247.38˚
\n" ); document.write( "v-u≈247.38-208.07≈39.31˚
\n" ); document.write( "tan(v-u)≈tan 39.31˚≈0.8188
\n" ); document.write( "cot(v-u)≈1/tan(v-u)≈1.2213
\n" ); document.write( "Exact value=171/140≈1.2214
\n" ); document.write( " \n" ); document.write( "
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