document.write( "Question 831818:

\n" ); document.write( "Given: \"cos%28A%29=-7%2F25\", \"pi+%3C+A+%3C+3pi%2F2\"
\n" ); document.write( " \"sin%28B%29=-3%2F5\", \"3pi%2F2+%3CB%3C2pi\"\r
\n" ); document.write( "\n" ); document.write( "Find: \"sin%28A-B%29\"
\n" ); document.write( " \"tan%28A-B%29\" \n" ); document.write( "

Algebra.Com's Answer #501808 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "Given: \"cos%28A%29=-7%2F25\", \"pi+%3C+A+%3C+3pi%2F2\" \r\n" );
document.write( "       \"sin%28B%29=-3%2F5\", \"3pi%2F2+%3CB%3C2pi\"\r\n" );
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document.write( "Find: \"sin%28A-B%29\"\r\n" );
document.write( "      \"tan%28A-B%29\"\r\n" );
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document.write( "\"cos%28A%29=-7%2F25\", \"pi+%3C+A+%3C+3pi%2F2\". That's Q3 \r\n" );
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document.write( "Draw the picture of angle A in the third quadrant Q3. \r\n" );
document.write( "Since the cosine is adjacent/hypotenuse or x/r, and since we are given \r\n" );
document.write( "\"cos%28A%29=-7%2F25\", make x=-7 and r=\"25\", and calculate y using the \r\n" );
document.write( "Pythagorean theorem:\r\n" );
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document.write( "    x²+y² = r²\r\n" );
document.write( " (-7)²+y² = 25²\r\n" );
document.write( "    49+y² = 625\r\n" );
document.write( "       y² = 576\r\n" );
document.write( "        y = ±√576\r\n" );
document.write( "        y = ±24, we take y = -24 \r\n" );
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document.write( "We take y negative because it goes down from the x-axis, \r\n" );
document.write( "and we ALWAYS take r positive because it begins on the\r\n" );
document.write( "right side of the x-axis and doesn't change its sign when\r\n" );
document.write( "it swings around into the other quadrants. \r\n" );
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document.write( "\"sin%28A%29=y%2Fr=%28-24%29%2F25=-7%2F25\"\r\n" );
document.write( "\"cos%28A%29=x%2Fr=%28-7%29%2F25=-7%2F25\"\r\n" );
document.write( "\"tan%28A%29=y%2Fx=%28-24%29%2F%28-7%29=7%2F24\"\r\n" );
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document.write( "\"sin%28B%29=-3%2F5\", \"3pi%2F2+%3CB+%3C+2pi\". That's Q4 \r\n" );
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document.write( "Draw the picture of angle B in the fourth quadrant Q4. Since the sine is\r\n" );
document.write( "opposite/hypotenuse or y/r, and since we are given  \"sin%28B%29=-3%2F5\",\r\n" );
document.write( "make y=-3 and r=5, and calculate x using the Pythagorean theorem:\r\n" );
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document.write( "    x²+y² = r²\r\n" );
document.write( " x²+(-3)² = 5²\r\n" );
document.write( "     x²+9 = 25\r\n" );
document.write( "       x² = 25\r\n" );
document.write( "        y = ±√25\r\n" );
document.write( "        y = ±5, we take y = -5 \r\n" );
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document.write( "We take y negative because it goes down from the x-axis, \r\n" );
document.write( "and we ALWAYS take r positive because it begins on the\r\n" );
document.write( "right side of the x-axis and doesn't change its sign when\r\n" );
document.write( "it swings around into the other quadrants. \r\n" );
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document.write( "-----------------------------------------------\r\n" );
document.write( "\"sin%28A%29=y%2Fr=%28-24%29%2F25=-24%2F25\"\r\n" );
document.write( "\"cos%28A%29=x%2Fr=%28-7%29%2F25=-7%2F25\"\r\n" );
document.write( "\"tan%28A%29=y%2Fx=%28-24%29%2F%28-7%29=24%2F7\"\r\n" );
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document.write( "--------------------------------------\r\n" );
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document.write( "\"sin%28B%29=y%2Fr=%28-3%29%2F5=-3%2F5\"\r\n" );
document.write( "\"cos%28B%29=x%2Fr=4%2F5\"\r\n" );
document.write( "\"tan%28B%29=y%2Fx=%28-3%29%2F-4=-3%2F4\"\r\n" );
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document.write( "Edwin
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