document.write( "Question 405450: Find the EXACT value of csc 495 degrees using reference angles. \n" ); document.write( "

Algebra.Com's Answer #286363 by Edwin McCravy(20059) $\"\"$ $\"About$

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document.write( "The angle 495° is more than one complete revolution counter-clockwise\r\n" );
document.write( "from the right side of the x-axis.  So we subtract 1 revolution or\r\n" );
document.write( "360° from 495° getting 135°.  So we can forget the first revolution.\r\n" );
document.write( "We now have just this:\r\n" );
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document.write( "Next we see that 135° is in the second quadrant. Let's indicate the \r\n" );
document.write( "reference angle in red, which is the smallest possible amout of \r\n" );
document.write( "rotation to get to the x-axis from the terminal side:\r\n" );
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document.write( "We subtract 135° from 180° to get 45°, which is the reference angle\r\n" );
document.write( "indicated by the red arc.\r\n" );
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document.write( "Now we remember our 45°-45°-90° right triangle:\r\n" );
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document.write( "The cosecant is the hypotenuse over the opposite which\r\n" );
document.write( "is  or just .  We remember that\r\n" );
document.write( "angles in the second quadrant have positive sines and cosecants,\r\n" );
document.write( "so the answer is\r\n" );
document.write( "               _\r\n" );
document.write( "csc(495°) = +Ö2\r\n" );
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document.write( "Edwin

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