document.write( "Question 141788: The point (0,-1) on the unit circle is rotated 315 degrees counter-clockwise. Determine the coordinates of the new point. \n" ); document.write( "
Algebra.Com's Answer #103454 by Edwin McCravy(20059)\"\" \"About 
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The point (0,-1) on the unit circle is rotated 315 degrees counter-clockwise.Determine the coordinates of the new point.\r
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document.write( "Now we subtract 315°-270° and find that the angle between the slanted\r\n" );
document.write( "radius and the left side of the x-axis is 45° (indicated by the green\r\n" );
document.write( "curved line, so we label it 45°:\r\n" );
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document.write( "Now from the point in question we draw a perpendicular up to the\r\n" );
document.write( "x-axis:\r\n" );
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document.write( "This forms a special right triangle.  \r\n" );
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document.write( "We are supposed to know that if a right triangle has an acute angle \r\n" );
document.write( "of 45°, then it is isosceles and the sides of the 45° angle are equal.\r\n" );
document.write( "The hypotenuse is the radius 1.\r\n" );
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document.write( "We can calculate the two equal sides of that right triangle by\r\n" );
document.write( "the Pythagorean theorem:\r\n" );
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document.write( "\"a%5E2%2Bb%5E2=c%5E2\"\r\n" );
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document.write( "Since we know that a = b we can substitute a for b: \r\n" );
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document.write( "\"a%5E2%2Ba%5E2=1%5E2\"\r\n" );
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document.write( "\"2a%5E2=1\"\r\n" );
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document.write( "\"a%5E2=1%2F2\"\r\n" );
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document.write( "\"a=sqrt%281%2F2%29\"\r\n" );
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document.write( "\"a=sqrt%28%281%2A2%29%2F%282%2A2%29%29\"\r\n" );
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document.write( "\"a=sqrt%282%29%2F2\" \r\n" );
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document.write( "So the vertical and horizontal sides of that right triangle \r\n" );
document.write( "are both equal to \"sqrt%282%29%2F2\".\r\n" );
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document.write( "The point is in the 3rd quadrant, so both its coordinates are\r\n" );
document.write( "negative, so the coordinates of the point is (\"-sqrt%282%29%2F2\",\"-sqrt%282%29%2F2\").\r\n" );
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document.write( "Edwin
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