document.write( "Question 1138000: If sin α = 4/5 and cos β = -5/13 for α in Quadrant I and β in Quadrant II, find cos(α - β). \n" ); document.write( "
Algebra.Com's Answer #755889 by Edwin McCravy(20063)\"\" \"About 
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document.write( "The formula is .\r\n" );
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document.write( "Draw angle α in Quadrant I:\r\n" );
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document.write( "Since sine = \"y%2Fr\", we make y=4 and r=5, so that the sin(α)\r\n" );
document.write( "will be \"y%2Fr\"\"%22%22=%22%22\"\"4%2F5\".\r\n" );
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document.write( "For the formula, we need sine and cosine, and the cosine is \"x%2Fr\"\r\n" );
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document.write( "So we find x by the Pythagorean relation: \r\n" );
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document.write( "\"x%5E2%2By%5E2=r%5E2\"\r\n" );
document.write( "\"x%5E2%2B%284%29%5E2=%285%29%5E2\"\r\n" );
document.write( "\"x%5E2%2B16=25\"\r\n" );
document.write( "\"x%5E2=9\"\r\n" );
document.write( "\"x+=+%22%22+%2B-+3\"\r\n" );
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document.write( "Since x goes to the right, we know to take the positive\r\n" );
document.write( "value \"x+=+%22%22%2B3\".  So now we know that \"cos%28alpha%29=x%2Fr=3%2F5\"\r\n" );
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document.write( "Next we draw angle β in Quadrant II:\r\n" );
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document.write( "Since cosine = \"x%2Fr\", we make x=-5 and r=13, so that the cos(β)\r\n" );
document.write( "will be \"x%2Fr\"\"%22%22=%22%22\"\"%28-5%29%2F13\".\r\n" );
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document.write( "For the formula, we need sine and cosine, and the sine is \"y%2Fr\"\r\n" );
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document.write( "So we find x by the Pythagorean relation: \r\n" );
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document.write( "\"x%5E2%2By%5E2=r%5E2\"\r\n" );
document.write( "\"%28-5%29%5E2%2By%5E2=%2813%29%5E2\"\r\n" );
document.write( "\"25%2By%5E2=169\"\r\n" );
document.write( "\"y%5E2=144\"\r\n" );
document.write( "\"y+=+%22%22+%2B-+12\"\r\n" );
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document.write( "Since y goes up from the x-axis, we know to take the positive\r\n" );
document.write( "value \"y+=+%22%22%2B12\".  So now we know that \"sin%28beta%29=y%2Fr=12%2F13\"\r\n" );
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document.write( "Now we use the formula\r\n" );
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document.write( ".\r\n" );
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document.write( "\"matrix%281%2C3%2Ccos%28alpha-beta%29%2C%22%22=%22%22%2C%28-15%2F65%29%2B%2848%2F65%29%29\"\r\n" );
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document.write( "\"matrix%281%2C3%2Ccos%28alpha-beta%29%2C%22%22=%22%22%2C33%2F65%29\"\r\n" );
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document.write( "Edwin
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