document.write( "Question 600374: simplify the expression: sin5pie/3 cos5pie/3-cos5pie/3 sin pie/3 \n" ); document.write( "
Algebra.Com's Answer #379295 by mamiya(56)\"\" \"About 
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you say sin(5pie/3) cos(5pie/3)-cos(5pie/3) sin (pie/3), but i think the question was rather
\n" ); document.write( "sin(5pie/3) cos(pie/3)-cos(5pie/3) sin (pie/3)\r
\n" ); document.write( "\n" ); document.write( "And if the question was what i just wrote , you do it this way.\r
\n" ); document.write( "\n" ); document.write( "first let take a look a those trigonometric formulas
\n" ); document.write( " sin(a+b) = sin(a) cos(b) + sin(b) cos(a)
\n" ); document.write( "sin(a-b) = sin(a) cos(b) - sin(b) cos(a)
\n" ); document.write( "Cos(a+b) = cos(a) cos(b) - sin(a) sin(b)
\n" ); document.write( "Cos(a-b) = cos(a) cos(b) + sin(a) sin(b)\r
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\n" ); document.write( "\n" ); document.write( "Now, let's get back to our problem
\n" ); document.write( " let's call 5pie/3 a and call pie/3 b
\n" ); document.write( "Then, sin5pie/3 cospie/3-cos5pie/3 sin pie/3= sin (a) cos(b)- cos(a) sin(b),
\n" ); document.write( "This looks like the second formula up above
\n" ); document.write( "so we get sin5pie/3 cospie/3-cos5pie/3 sin pie/3 = Sin ( a-b)
\n" ); document.write( " and we know for this case that a = 5pie\3 and b=pie/3
\n" ); document.write( "so, sin5pie/3 cospie/3-cos5pie/3 sin pie/3 = Sin ( 5pie/3 - pie/3)
\n" ); document.write( " = sin ( 4pie/3)
\n" ); document.write( " = -(sqrt(3))/2\r
\n" ); document.write( "\n" ); document.write( "So the anwer is Sin( 4pie/3) and if you want to go further and find its value it is -(sqrt(3))/2
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