document.write( "Question 134127: Used the symbol @ for the regular symbol.\r
\n" ); document.write( "\n" ); document.write( "Given that cos@ = - 4/5 and @ is in Quadrant 2, find:\r
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Algebra.Com's Answer #98114 by Edwin McCravy(20060) $\"\"$ $\"About$

You can put this solution on YOUR website!

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document.write( "(I'll use Q instead of @, so my computer won't think it's \r\n" );
document.write( "an email address. Igor hasn't put in the Greek letter \"theta\"\r\n" );
document.write( "in his program.  Think I'll ask him to put it in.)\r\n" );
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document.write( "Given that cosQ =  and Q is in Quadrant 2, find: \r\n" );
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document.write( "Draw the picture of Q.  We use the numerator and denominator\r\n" );
document.write( "of  for x and r.  Since , to put \r\n" );
document.write( "q in Quadrant 2, we must take x as  and  as ,\r\n" );
document.write( "and draw this picture, with the curved line indicating angle Q: \r\n" );
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document.write( "Now we use the Pythagorean theorm to find \r\n" );
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document.write( "±\r\n" );
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document.write( "But since  goes upward from the x-axis,\r\n" );
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document.write( "we take the positive value, so \r\n" );
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document.write( "To find\r\n" );
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document.write( "sinQ, we only need to know that sinQ =  or  \r\n" );
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document.write( "To find\r\n" );
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document.write( "sin2Q, we need the identity sin2A = 2sinAcosA\r\n" );
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document.write( "sin2Q = 2sinQcosQ\r\n" );
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document.write( "sin2Q = 2\r\n" );
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document.write( "sin2Q = \r\n" );
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document.write( "To find\r\n" );
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document.write( "cos3Q, we need the identities cos(A+B) = cosAcosB - sinAsinB and cos2A = 2cos²A-1  \r\n" );
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document.write( "First we rewrite 3Q as 2Q+Q\r\n" );
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document.write( "Then by the first identity,\r\n" );
document.write( "cos3Q = cos(2Q+Q) = cos2QcosQ - sin2QsinQ\r\n" );
document.write( "= cos2Q() - sin2Q()\r\n" );
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document.write( "and we have already found sin2Q to be ,\r\n" );
document.write( "so\r\n" );
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document.write( "= cos2Q() - ()\r\n" );
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document.write( "= ()cos2Q - ()\r\n" );
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document.write( "= cos2Q + \r\n" );
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document.write( "Now we use the second identity to rewrite cos2Q \r\n" );
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document.write( "= (2cos²Q - 1) + \r\n" );
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document.write( "Distribute:\r\n" );
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document.write( "= (2cos²Q) +  + \r\n" );
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document.write( "= cos²Q +  + \r\n" );
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document.write( "Combine the last two terms and substitute  for cosQ\r\n" );
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document.write( "=  +  = \r\n" );
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document.write( "=  + \r\n" );
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document.write( "=  + \r\n" );
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document.write( "= \r\n" );
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document.write( "To find , we use the identity  = \r\n" );
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document.write( " = \r\n" );
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document.write( "= \r\n" );
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document.write( "= \r\n" );
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document.write( "= \r\n" );
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document.write( "= \r\n" );
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document.write( "= \r\n" );
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document.write( "= \r\n" );
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document.write( "= \r\n" );
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document.write( "To find sin(Q + 60°) we use identity  sin(A + B) = sinAcosB + cosAsinB\r\n" );
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document.write( "sin(Q + 60°) = sinQcos60° + cosQsin60°\r\n" );
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document.write( "Now we use the fact that cos60° = , sin60° = , cosQ =  and sinQ = \r\n" );
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document.write( "sin(Q + 60°) =  =\r\n" );
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document.write( " =\r\n" );
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document.write( "Edwin

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