document.write( "Question 1158028: determine the specified trigonometric ratio for each angle with a terminal side that passes through the given point. \r
\n" ); document.write( "\n" ); document.write( "1.Sin0; (-8,6)
\n" ); document.write( "2.csc0; (2,-1)
\n" ); document.write( "3.tan0;(0,1)
\n" ); document.write( "4.cos0; (-4,-2) \n" ); document.write( "
Algebra.Com's Answer #854540 by KMST(5377)\"\" \"About 
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The standard position of an angle is vertex at the origin, initial side along the positive x-axis.
\n" ); document.write( "We measure angles counterclockwise, and could define an angle measure as negative or greater than 360 degree,
\n" ); document.write( "but the trigonometric functions only care about the position of the terminal side.
\n" ); document.write( "I will assume \"0%5Eo%3C=theta%3C360%5Eo\" for all angles.
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\n" ); document.write( "Terminal side passing through \"P%28-8%2C6%29\" :
\n" ); document.write( " There is a large right triangles with hypotenuse \"OP\" and a similar triangle whose hypotenuse, \"OA\" , is a radius of the unit circle shown in red.
\n" ); document.write( "The large one has legs of length \"8\" and \"6\" , and hypotenuse \"OP=sqrt%286%5E2%2B8%5E2%29=10\" . The length of the small right triangle's hypotenuse, \"OA=1\"} ,is 10 times smaller, and so are the legs.
\n" ); document.write( "The function \"sin%28green%28theta%29%29\" is defined as the y-coordinate of point A, \"sin%28green%28theta%29%29=highlight%280.6%29\" , and \"cos%28green%28theta%29%29\" is defined as the x-coordinate of point A, \"cos%28green%28theta%29%29=-0.8\" .
\n" ); document.write( "We can calculate \"sin%28red%28alpha%29%29=6%2F10=0.6\" as a trigonometric ratio. and determine that \"red%28alpha%29=36.9%5Eo\".
\n" ); document.write( "\"green%28theta%29=180%5Eo-36.9%5Eo=143.1%5Eo\"
\n" ); document.write( "Trigonometric cosine and sine functions of \"green%28theta%29\" , defined as the x-coordinate and the y-coordinate of point A respectively are numerically the same as those for \"red%28alpha%29\" , but may be positive or negative depending on the quadrant.
\n" ); document.write( "The sign will be the same for coordinates of any point on the terminal side.
\n" ); document.write( "
\n" ); document.write( "Terminal side passing through \"P%282%2C-1%29\" :
\n" ); document.write( "\"P%282%2C-1%29\" is in quadrant IV, with positive x-coordinate, so \"cos%28theta%29=cos%28alpha%29%3E0\".
\n" ); document.write( "The large right triangle, in this case, has leg lengths of 2, and 1, and a hypotenuse length of \"OP=sqrt%282%5E2%2B1%5E3%29=sqrt%284%2B1%29=sqrt%285%29\" .
\n" ); document.write( "\"cos%28theta%29=cos%28alpha%29=2%2Fsqrt%285%29\" and \"sec%28theta%29=1%2Fcos%28theta%29=highlight%28sqrt%285%29%2F2=1.118%29\"(rounded)
\n" ); document.write( "The angles involved would be \"alpha=26.56%5Eo\" , \"theta=360%5Eo-26.56%5Eo=333.44%5Eo\"
\n" ); document.write( "
\n" ); document.write( "Terminal side passing through \"P%280%2C1%29\" :
\n" ); document.write( "P is on the unit circle, so its x-coordinate and y-coordinate are \"cos%28theta%29\" and \"sin%28theta%29\" respectively.
\n" ); document.write( "\"cos%28theta%29=0\" , \"sin%28theta%29=1\" and \"tan%28theta%29=sin%28theta%29%2Fcos%28theta%29\" is undefined.
\n" ); document.write( "
\n" ); document.write( "Terminal side passing through \"P%28-4%2C-2%29\" :
\n" ); document.write( "Booth coordinates are negative, and so will be sine and cosine.
\n" ); document.write( "OP would be the hypotenuse of a right triangle with leg lengths 4, and 2.
\n" ); document.write( "The hypotenuse length is
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