document.write( "Question 1205032: If sin(x)=-5/13 and x is in quadrant III, with 0° ≤ x < 360°, find the exact values of the expressions without solving for x.
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Algebra.Com's Answer #841631 by Edwin McCravy(20060) $\"\"$ $\"About$

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If sin(x)=-5/13 and x is in quadrant III,...
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document.write( "So for angle x, we have a 5-12-13 right triangle in quadrant III,\r\n" );
document.write( "where x=-12, y=-5, and r=+13.\r\n" );
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document.write( "There is often a conflict of notation when x is used for an angle, and also\r\n" );
document.write( "for values of the adjacent side of the defining right triangle. There is a\r\n" );
document.write( "problem here. But I think you won't get confused.  Teachers aren't always\r\n" );
document.write( "careful to point out this conflict, which happens a lot. (just like the problem\r\n" );
document.write( "of how to say \"the sign of the sine\". J )\r\n" );
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document.write( "So cos(x)=x/r=(-12)/(+13)=-12/13 and tan(x)=y/x=(-5)/(-12)=+5/12\r\n" );
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document.write( " so x/2 is in quadrant II (the upper half of quadrant II).\r\n" );
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document.write( "So sin(x/2) is positive, cos(x/2) is negative, and tan(x/2) is negative.\r\n" );
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document.write( "So we just use the half-angle formulas:\r\n" );
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document.write( "We know to use the + because x/2 is in quadrant II, where sine is positive.\r\n" );
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document.write( "We know to use the - because x/2 is in quadrant II, where cosine is negative.\r\n" );
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document.write( "Now we could use a formula for tan(x/2), but now all we need is \r\n" );
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document.write( "Edwin

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