document.write( "Question 1099671: the point (4, -6) in on the terminal side of an angle t. find cos(t) to 2 decimal places. \n" ); document.write( "
Algebra.Com's Answer #714135 by Edwin McCravy(20060) $\"\"$ $\"About$
You can put this solution on YOUR website!
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document.write( "Plot the point (4,-6)\r\n" );
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document.write( "Next draw a line from the origin down to that point (in green).\r\n" );
document.write( "That's the terminal side.\r\n" );
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document.write( "Now indicate the positive angle t by drawing an arc starting at\r\n" );
document.write( "the right hand side of the x-axis and swinging around counter-\r\n" );
document.write( "clockwise to the green line (in red):\r\n" );
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document.write( "Now draw a horizontal line from the point (4,-6) to the x-axis \r\n" );
document.write( "(in blue):\r\n" );
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document.write( "Notice that you now have a right triangle.  Label the horizontal \r\n" );
document.write( "side of that right triangle as x equal to the x-coordinate of\r\n" );
document.write( "the point (4,-6), x=4.  Also label the vertical (blue) side of\r\n" );
document.write( "that right triangle as y equal to the y-coordinate of\r\n" );
document.write( "the point (4,-6), y=-6.\r\n" );
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document.write( "  \r\n" );
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document.write( "Next we calculate the hypotenuse of the right triangle, which is\r\n" );
document.write( "the green side and the terminal side of angle t, by using the\r\n" );
document.write( "Pythagorean theorem.  But we label that green side r, because we\r\n" );
document.write( "think of it as a radius swinging around forming the angle t.\r\n" );
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document.write( "(We always take r as a positive number, since it was positive\r\n" );
document.write( "before it swung around to form the angle t). We label the green\r\n" );
document.write( "side as .  [Didn't have much room to write it :)].\r\n" );
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document.write( "We use the REFERENCE angle to determine which sides are which. \r\n" );
document.write( "The REFERENCE angle is the angle INSIDE the triangle that has\r\n" );
document.write( "one side as the x-axis.  We see that the adjacent side is x=4,\r\n" );
document.write( "the opposite side is y=-6, and the hypotenuse is .\r\n" );
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document.write( "We are asked to find the cosine of the angle t.  Now we remember\r\n" );
document.write( "that . So we write:\r\n" );
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document.write( "But the denominator needs to be rationalized, so we multiply by .\r\n" );
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document.write( "That's the simplest radical form.  But I just noticed that you are\r\n" );
document.write( "asked to get a calculator and round it to 2 decimal places.  So we\r\n" );
document.write( "get 0.5547001962 and round it to 0.55.\r\n" );
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document.write( "Edwin
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