document.write( "Question 1107160: solve equation sin x=0.5 where 0 < x < 360° \n" ); document.write( "
Algebra.Com's Answer #722155 by Edwin McCravy(20065)\"\" \"About 
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sin x = 0.5
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document.write( "That involves a special angle.\r\n" );
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document.write( "You need to learn these three special right triangles, \r\n" );
document.write( "their sides, and their angles\r\n" );
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document.write( "Make the 0.5 into a fraction\r\n" );
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document.write( "sin x = 0.5 = 1/2 = opposite/hypotenuse\r\n" );
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document.write( "The fraction 1/2 has 1 for the numerator and 2 for the denominator.\r\n" );
document.write( "Which one of those right triangles has 1 for the opposite side and 2\r\n" );
document.write( "for the hypotenuse? It's this one:\r\n" );
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document.write( "The sine is positive in QI and QII\r\n" );
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document.write( "So we put that triangle into QI and QII, and we indicate the \r\n" );
document.write( "counter-clockwise rotation from the right side of the x-axis \r\n" );
document.write( "with a red arc:\r\n" );
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document.write( "Putting it in QI, we have this:\r\n" );
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document.write( "The red arc tells us that the counter-clockwise rotation from\r\n" );
document.write( "the right side of the x-axis is through 30°, so the QI answer is\r\n" );
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document.write( "x = 30°\r\n" );
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document.write( "Now let's put that triangle in QII, notice that since the\r\n" );
document.write( "adjacent side goes left of the origin, we must change the sign\r\n" );
document.write( "of \"sqrt%283%29\" to \"-sqrt%283%29\"\r\n" );
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document.write( "Now the red arc that measures the counter-clockwise rotation \r\n" );
document.write( "from the right side of the x-axis.  But it is not 30°, for 30°\r\n" );
document.write( "is the reference angle.  The angle of the red arc is 180°-30°,\r\n" );
document.write( "or 150°.\r\n" );
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document.write( "So the QII answer is\r\n" );
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document.write( "x = 150°.\r\n" );
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document.write( "Edwin
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