document.write( "Question 849991: a and b are quadrant 1 angles with cos(a)=15/17 and csc(b)=41/9 find sin (a+b).\r
\n" ); document.write( "\n" ); document.write( "answer options are a. 185/697 b. 455/697 c. 528/697 d. 672/697\r
\n" ); document.write( "\n" ); document.write( "I receive the demonator of 697 but can not find the numerator \n" ); document.write( "

Algebra.Com's Answer #511945 by AnlytcPhil(1810) $\"\"$ $\"About$

You can put this solution on YOUR website!

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document.write( "We have to graph the two first quadrant angles, A and B.\r\n" );
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document.write( "Let's draw A first:\r\n" );
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document.write( "We are given this\r\n" );
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document.write( "We know that  or \r\n" );
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document.write( "So we make the adjacent side, x, of A in the right triangle equal to the \r\n" );
document.write( "numerator of , which is 15.  We make the hypotenuse, r,\r\n" );
document.write( "of the right triangle equal to the denominator of the fraction,\r\n" );
document.write( "which is 17. But we don't yet know y, so we put \"y=? at first.\r\n" );
document.write( "Like this:\r\n" );
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document.write( "Next we find y by the Pythagorean theorem\r\n" );
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document.write( " r² = x²+y²\r\n" );
document.write( "17² = 15²+y²\r\n" );
document.write( "289 = 225+y²\r\n" );
document.write( " 64 = y²\r\n" );
document.write( "  8 = y \r\n" );
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document.write( "So we can erase the question mark and put 8 in its place\r\n" );
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document.write( "Now let's draw to other first quadrant angle B :\r\n" );
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document.write( "We are given this\r\n" );
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document.write( "We know that  or \r\n" );
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document.write( "So we make the hypotenuse of the right triangle r, equal to the \r\n" );
document.write( "numerator of , which is 41.  We make the opposite side\r\n" );
document.write( "of the right triangle equal to the denominator of the fraction,\r\n" );
document.write( "which is 9. But we don't yet know x, so we put \"x=? at first.\r\n" );
document.write( "Like this:\r\n" );
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document.write( "Next we find x by the Pythagorean theorem\r\n" );
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document.write( "  r² = x²+y²\r\n" );
document.write( " 41² = x²+9²\r\n" );
document.write( "1681 = x²+81\r\n" );
document.write( "1600 = x²\r\n" );
document.write( "  40 = x\r\n" );
document.write( "  \r\n" );
document.write( "So we can erase the question mark and put 40 in its place:\r\n" );
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document.write( "Now that we have x = adjacent, y = opposite, and r = hypotenuse for\r\n" );
document.write( "both angles A and B, now we can proceed to find sin(A+B)  \r\n" );
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document.write( "Let's put both graphs here for convenience:\r\n" );
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document.write( "  \r\n" );
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document.write( "The identity for sin(A+B) is\r\n" );
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document.write( "sin(A+B) = sin(A)cos(B)+cos(A)sin(B)\r\n" );
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document.write( "sin(A) =  =  = \r\n" );
document.write( "cos(A) =  =  = \r\n" );
document.write( "sin(B) =  =  = \r\n" );
document.write( "cos(A) =  =  = \r\n" );
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document.write( "Plug in:\r\n" );
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document.write( "sin(A+B) = sin(A)cos(B)+cos(A)sin(B)\r\n" );
document.write( "sin(A+B) =  =  = \r\n" );
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document.write( "Edwin

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