document.write( "Question 1116854: Find the values of the trigonometric functions of t from the given information.
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Algebra.Com's Answer #731768 by Edwin McCravy(20060) $\"\"$ $\"About$

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Find the values of the trigonometric functions of t from the given information.
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document.write( "3 is a positive number.  The cosecant is positive in QI and QII.\r\n" );
document.write( "The cosine is negative in QII and QIII.  Therefore t must be in\r\n" );
document.write( "QII.\r\n" );
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document.write( "The cosecant is r/y or the hypotenuse over the opposite.  Therefore we\r\n" );
document.write( "take 3 as the fraction 3/1 and consider the r=3 as the hypotenuse, \r\n" );
document.write( "which is ALWAYS taken positive, and y=1 as the opposite.  We use the Pythagorean theorem:\r\n" );
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document.write( "(hypotenuse)² = (adjacent)² + (opposite)²\r\n" );
document.write( "           r² = x² + y²\r\n" );
document.write( "           3² = x² + 1²\r\n" );
document.write( "            9 = x² + 1\r\n" );
document.write( "            8 = x²\r\n" );
document.write( "          ±√8 = x\r\n" );
document.write( "         ±2√2 = x\r\n" );
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document.write( "In QII the adjacent = x is negative, so we take the negative sign\r\n" );
document.write( "x = -2√2.\r\n" );
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document.write( "adjacent = x = -2√2,  opposite = y = 1, hypotenuse = r = 3\r\n" );
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document.write( "sin(t) = opposite/hypotenuse = y/r = 1/3\r\n" );
document.write( "cos(t) = adjacent/hypotenuse = x/r = -2√2/3 \r\n" );
document.write( "tan(t) = opposite/adjacent = y/x = 1/(-2√2) = [1/(-2√2)][√2/√2] = \r\n" );
document.write( "       = (√2)/(-2∙2) = -√2/4 \r\n" );
document.write( "sec(t) = hypotenuse/adjacent = r/x = 3/[-2√2] = [3/(-2√2)][√2/√2] = \r\n" );
document.write( "       = (3√2)/(-2∙2) = -3√2/4\r\n" );
document.write( "csc(t) = hypotenuse/opposite = r/y = 3/1 = 3 (given!)\r\n" );
document.write( "cot(t) = adjacent/opposite = x/y = -2√2/1 = -2√2\r\n" );
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document.write( "Edwin

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