document.write( "Question 627577: What values for q (0 Ł q < 2p) satisfy the equation? \r
\n" ); document.write( "\n" ); document.write( "2sqrt2sinq + 2 = 0 \n" ); document.write( "

Algebra.Com's Answer #395076 by jsmallt9(3758) $\"\"$ $\"About$

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$\"2sqrt%282%29sin%28q%29+%2B+2+=+0\"$
\n" ); document.write( "First we solve for sin(q). Subtracting 2:
\n" ); document.write( " $\"2sqrt%282%29sin%28q%29+=+-2\"$
\n" ); document.write( "Divide both sides by $\"2sqrt%282%29\"$ :
\n" ); document.write( " $\"sin%28q%29+=+-1%2Fsqrt%282%29\"$
\n" ); document.write( "Rationalizing the denominator:
\n" ); document.write( " $\"sin%28q%29+=+%28-1%2Fsqrt%282%29%29%28sqrt%282%29%2Fsqrt%282%29%29\"$
\n" ); document.write( " $\"sin%28q%29+=+-sqrt%282%29%2F2\"$
\n" ); document.write( "Now we solve for q. We should recognize $\"-sqrt%282%29%2F2\"$ as a special angle value for sin. We should recognize that the reference angle will be $\"pi%2F4\"$ . And since our sin is negative and since sin is negative in the 3rd and fourth quadrants, we know that q must terminate there, too, with a reference angle of $\"pi%2F4\"$
\n" ); document.write( "So
\n" ); document.write( " $\"q+=+pi+%2B+pi%2F4+=+4pi%2F4+%2B+pi%2F4+=+5pi%2F4\"$ (for the third quadrant)
\n" ); document.write( "or
\n" ); document.write( " $\"q+=+2pi+-+pi%2F4+=+8pi%2F4+-+pi%2F4+=+7pi%2F4\"$ (for the fourth quadrant) \n" ); document.write( "

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