document.write( "Question 937178: What is the coordinates of the point of intersection of the terminal side of -300° angle on the unit circle? \n" ); document.write( "

Algebra.Com's Answer #570645 by Edwin McCravy(20055) $\"\"$ $\"About$

You can put this solution on YOUR website!
Sorry! She's wrong!
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document.write( "She's right about the x and y coordinates being respectively \r\n" );
document.write( "the cosine and sine of the angle.  But she gave you the wrong \r\n" );
document.write( "signed y-coordinate, because she didn't draw the graph.  Mathematics\r\n" );
document.write( "is all about graphs.  One should always draw graphs, especially\r\n" );
document.write( "in trigonometry problems.\r\n" );
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document.write( "Below is the graph of what you should draw first.  Since -300° is a \r\n" );
document.write( "negative angle, it is formed by a CLOCKWISE rotation of 300 \r\n" );
document.write( "degrees from the right side of the x-axis.  That rotation is \r\n" );
document.write( "indicated by the red arc drawn CLOCKWISE from the right side\r\n" );
document.write( "of the x-axis to the terminal side. \r\n" );
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document.write( "So it ends up in the first quadrant, not the fourth, like the other\r\n" );
document.write( "tutor thought. The coordinates of the point of \r\n" );
document.write( "intersection is \r\n" );
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document.write( "but you have to simplify it.  Here's how:\r\n" );
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document.write( "To simplify the coordinates, draw a radius to the point, and\r\n" );
document.write( "a vertical line up to the point forming a reference right triangle.\r\n" );
document.write( "Since the red arc is 300°, and a complete revolution is 360°, the\r\n" );
document.write( "angle inside the reference right triangle is 360°-300°=60°. The\r\n" );
document.write( "radius is its hypotenuse. That makes the reference triangle a \r\n" );
document.write( "30-60-90 right triangle.   \r\n" );
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document.write( "So the correct coordinate for the point is .\r\n" );
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document.write( "Edwin

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