document.write( "Question 1117589: If secA=13/5 with A in quadrant 4 and tanB=-3/4 with B in quadrant 2, find the exact value of sin(A+B)\r
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Algebra.Com's Answer #732756 by KMST(5328) $\"\"$ $\"About$

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WHAT YOU NEED TO KNOW:
\n" ); document.write( "For any angle $\"theta\"$ , if $\"cos%28theta%29%3C%3E0\"$ , $\"sec%28theta%29\"$ $\"%22=%22\"$ $\"1%2Fcos%28theta%29\"$ ,
\n" ); document.write( "and $\"tan%28theta%29\"$ $\"%22=%22\"$ $\"sin%28theta%29%2Fcos%28theta%29\"$ .
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\n" ); document.write( "For any angle $\"theta\"$ , $\"cos%28theta%29%2Bsin%28theta%29=1\"$ .
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\n" ); document.write( "If $\"theta\"$ is in quadrant IV (four), $\"cos%28theta%29%3E0\"$ and $\"sin%28theta%29%3C0\"$ .
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\n" ); document.write( "For any angles $\"A\"$ and $\"B\"$ , $\"sin%28A%2BB%29\"$ $\"%22=%22\"$ $\"cos%28A%29sin%28B%29%2Bsin%28A%29cos%28B%29\"$
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\n" ); document.write( "WHAT COULD ALSO HELP:
\n" ); document.write( "Because teachers like problems with answers that are integer or rational numbers,
\n" ); document.write( "they often use right triangles with integer side lengths.
\n" ); document.write( "The three side length form what we call a Pythagorean triple,
\n" ); document.write( "like (3,4,5), (5,12,13), (8,15,17), or (7,24,25).
\n" ); document.write( "If you do not need to \"show all of your work\", those triangles save you time.
\n" ); document.write( "If you have to show all of your work, those triangles provide a good check.
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\n" ); document.write( "For example,

. For that $\"theta\"$ in quadrant I, $\"system%28cos%28theta%29=4%2F5%2Csin%28theta%29=3%2F5%2Ctan%28theta%29=3%2F4%29\"$ .
\n" ); document.write( "The angle $\"B\"$ from your problem, in quadrant II, has $\"theta\"$ as its reference angle,
\n" ); document.write( "so $\"system%28cos%28B%29=-4%2F5%2Csin%28B%29=3%2F5%2Ctan%28B%29=-3%2F4%29\"$ .
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\n" ); document.write( "Also, for A in quadrant IV, the reference angle is $\"alpha\"$ shown below.
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so $\"system%28cos%28alpha%29=5%2F13%2Csin%28alpha%29=12%2F13%2Csec%28alpha%29=13%2F5%29\"$ ,
\n" ); document.write( "so for A in quadrant IV, $\"system%28cos%28A%29=5%2F13%2Csin%28A%29=-12%2F13%2Csec%28A%29=13%2F5%29\"$ . \n" ); document.write( "

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