document.write( "Question 1060955: Solve the equation over the interval {0, 360). \r
\n" ); document.write( "\n" ); document.write( "The answer to this problem, according to the back of my book, is {57.7, 159.2}. (Degrees, of course). \r
\n" ); document.write( "\n" ); document.write( "Now, the problem:\r
\n" ); document.write( "\n" ); document.write( "cot( x ) + 2csc( x ) = 3\r
\n" ); document.write( "\n" ); document.write( "What I started off doing is changing everything to sin and cos. \r
\n" ); document.write( "\n" ); document.write( "So we have:\r
\n" ); document.write( "\n" ); document.write( "cos( x ) / [sin( x )] + 2 / sin( x ) = 3\r
\n" ); document.write( "\n" ); document.write( "Since sin( x ) is our common denominator, we have:\r
\n" ); document.write( "\n" ); document.write( "cos( x ) + 2 / sin( x ) = 3\r
\n" ); document.write( "\n" ); document.write( "Multiply each side by sin( x ).\r
\n" ); document.write( "\n" ); document.write( "cos( x ) + 2 = 3sin( x ). \r
\n" ); document.write( "\n" ); document.write( "Now, I don't know where to go from here. Help, please! \n" ); document.write( "

Algebra.Com's Answer #675784 by ikleyn(52908) $\"\"$ $\"About$

You can put this solution on YOUR website!
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document.write( "cos( x ) + 2 = 3sin( x )   --->  (square both sides)   --->  \r\n" );
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document.write( " =   --->  (replace sin^2(x) by 1-cos^2(x) )  --->  \r\n" );
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document.write( " =   --->\r\n" );
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document.write( " = 0.\r\n" );
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document.write( "Introduce new variable z = cos(x). Your last equation becomes\r\n" );
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document.write( " = 0.\r\n" );
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document.write( "It is a quadratic equation. Solve it for z using the quadratic formula. You will get\r\n" );
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document.write( " =  = .  \r\n" );
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document.write( " =  0.539.  --->  x = arccos(0.539) = 1.006 rad = 57.7 degree.\r\n" );
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document.write( " = -0.935.  --->  x =  - arccos(0.935) = 2.778 rad = 159.2 degree.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Plot y = cos(x) + 2 and y = 3sin(x)\r
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