document.write( "Question 968978: if sine theta = -4/7 and is in quadrant 3, then the sum of sine theta + sine (theta-pie)+sine(2pie+theta) is? \n" ); document.write( "

Algebra.Com's Answer #854542 by ikleyn(53875) $\"\"$ $\"About$

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\n" ); document.write( "if sine theta = -4/7 and is in quadrant 3, then the sum of sine theta + sine (theta-pie)+sine(2pie+theta) is?
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\n" ); document.write( "\n" ); document.write( " This problem allows and assumes much simpler solution comparing with that in the post by @lwsshak3.\r
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document.write( "Second addend, , has the opposite value to the first addend, .\r\n" );
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document.write( "Therefore , when added, these two addends mutually cancel each other, giving 0 (zero).\r\n" );
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document.write( "Thus the sum of the first two addends vanishes, and the given expression is reduced to the last single term\r\n" );
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document.write( "        ,\r\n" );
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document.write( "which, due to the periodicity of function sin, is simply sin(theta), which is -4/7 (given in the problem).\r\n" );
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document.write( "So, the ANSWER to the problem's question is -4/7.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved in a simple way, without any calculations, using the basic properties of function sin.\r
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\n" ); document.write( "\n" ); document.write( "I am 127% sure that this is the desired and the expected method of solution to the given problem.\r
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