Algebra.Com's Answer #782284 by Edwin McCravy(20086)![\"\"](\"/images/stars/stars-13.gif\")  
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If tan α = − 4/3 and cot β = 15/8
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document.write( " for a second-quadrant angle α and a third-quadrant angle β, find the following.
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document.write( "1. sin (a+b)
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document.write( "2. cos (a+b)
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document.write( "3. tan (a+b)\r
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document.write( "I got -5 for #1, 20 for #2, and 13/84 for #3. They are all wrong and I do not know why. Maybe because I just substituted the fractions I was given into the equations? \r
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document.write( "We draw a picture of α in Quadrant II, and a picture of β in Quadrant III\r\n" );
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document.write( "From the ends of the terminal sides we draw vertical lines to the x-axis,\r\n" );
document.write( "in green, forming right triangles:\r\n" );
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document.write( "We are given that tan α = − 4/3\r\n" );
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document.write( "Since we know that TANGENT = OPPOSITE/ADJACENT = y/x, we label the\r\n" );
document.write( "opposite side (y) as the numerator of -4/3, which is -4, negative because\r\n" );
document.write( "it goes left. We label the adjacent (x) as the denominator of -4/3,\r\n" );
document.write( "which is +3 because it goes upward from the x-axis. \r\n" );
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document.write( "We are given that cot(β)= 15/8\r\n" );
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document.write( "Since we know that COTANGENT = ADJACENT/OPPOSITE = x/y, we label the\r\n" );
document.write( "adjacent side (x) as the numerator of 15/8, thought of as (-15)/(-8) which is\r\n" );
document.write( "-15, negative because\r\n" );
document.write( "it goes downward. We label the opposite (y) as the denominator of (-15)/(-8),\r\n" );
document.write( "which is -8 because it goes left.\r\n" );
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document.write( "Next we find the missing sides, the terminal sides, using the Pythagorean theorem:\r\n" );
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document.write( "Note that we always take the terminal side r as positive.\r\n" );
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document.write( "Now we're finally ready to calculate\r\n" );
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document.write( "1. sin (a+b)\r\n" );
document.write( "2. cos (a+b)\r\n" );
document.write( "3. tan (a+b) \r\n" );
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document.write( "where\r\n" );
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document.write( "and\r\n" );
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document.write( "Edwin \n" );
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