document.write( "Question 1158249: Solve the given equation. (Enter your answers as a comma-separated list. Let k be any integer. Round terms to two decimal places where appropriate.)
\n" ); document.write( "sin(θ) = − sqr2/2
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Algebra.Com's Answer #781178 by Theo(13342)\"\" \"About 
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sin(theta) = -sqrt(2)/2
\n" ); document.write( "to find the equivalent angle in the first quadrant, solve for sin(theta) = sqrt(2)/2
\n" ); document.write( "that makes theta equal to 45 degrees.
\n" ); document.write( "the sine of 45 degrees is positive in the first quadrant and the second quadrant.
\n" ); document.write( "it is negative in the third quadrant and the fourth quadrant.
\n" ); document.write( "therefore, for 0 <= x <= 360 degrees, the angle will be:
\n" ); document.write( "180 + 45 = 225 degrees in the third quadrant.
\n" ); document.write( "360 - 45 = 315 degrees in the fourth quadrant.
\n" ); document.write( "this repeats every 360 degrees, therefore, the complete answer is:
\n" ); document.write( "225 plus or minus k * 360 degrees and 315 plus or minus k * 360 degrees.
\n" ); document.write( "i don't remember, and i can't find the reference, but this may be able to be written as {225,315} plus or minus k * 360.
\n" ); document.write( "on a graph, this would look like this.\r
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\n" ); document.write( "\n" ); document.write( "the example shows that y = -sqrt(2)/2 occurs at:
\n" ); document.write( "225 degrees and 315 degrees when k = 1
\n" ); document.write( "1305 degrees and 1390 degrees when k = 3
\n" ); document.write( "-855 degrees and -765 degrees when -k = -3
\n" ); document.write( "the sine wave function repeats forever in each direction every 360 degrees.
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