document.write( "Question 1030548: A is an angle in quadrant 2. TanA = -3/root5. Solve the following and rationalize the denominator to the exact value.
\n" ); document.write( "a) Sin2A
\n" ); document.write( "b) Cos 2A
\n" ); document.write( "c) Cos(A + pi/2)
\n" ); document.write( "d) Sin(A + pi/2) \n" ); document.write( "

Algebra.Com's Answer #645398 by ikleyn(52803) $\"\"$ $\"About$

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\n" ); document.write( "A is an angle in quadrant 2. TanA = -3/root5. Solve the following and rationalize the denominator to the exact value.
\n" ); document.write( "a) Sin2A
\n" ); document.write( "b) Cos 2A
\n" ); document.write( "c) Cos(A + pi/2)
\n" ); document.write( "d) Sin(A + pi/2)
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document.write( "First of all, we need to find  sin(A)  and  cos(A)  based on the given value of tan(A) and the fact that angle A is in quadrant 2.\r\n" );
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document.write( "For it, we will use well known formulas  of Trigonometry \r\n" );
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document.write( " =   and   = .\r\n" );
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document.write( "Since tan(A) = , we have \r\n" );
document.write( "sin(A) =  =  =  =  =      and \r\n" );
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document.write( "cos(A) = - = - = - = - = .\r\n" );
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document.write( "The sign for sin(A) is \"+\" since the angle A is in Q2.  The sign for cos(A) is \"-\" due to the same reason.\r\n" );
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document.write( "Now\r\n" );
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document.write( "a)  sin(2A) = 2*sin(a)*cos(A) =  =  =  = .\r\n" );
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document.write( "b)  cos(2A) =  =  =  = .\r\n" );
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document.write( "    (By the way, the fact that cos(2A) is negative means that the angle 2A is in Q3).\r\n" );
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document.write( "c)  cos(A + pi/2) = -sin(A) = -.\r\n" );
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document.write( "d)  sin(A + pi/2) = cos(A) = .\r\n" );
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document.write( "The problem is solved. \r\n" );
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