document.write( "Question 644062: please help me solve this Evaluate (if possible) the six trigonometric functions of the real number. (If not possible, enter IMPOSSIBLE.)
\n" ); document.write( "t = −π \n" ); document.write( "
Algebra.Com's Answer #404868 by KMST(5328)\"\" \"About 
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Trigonometric functions are defined based on a set of x-y coordinates and the unit circle.
\n" ); document.write( "The unit circle (with radius=1) is centered at point O(0,0), the origin.
\n" ); document.write( "Angles are considered as clockwise or counterclockwise turns from a starting side placed over the positive x-axis, as ray OA in the figure below.
\n" ); document.write( "The starting side is always in that standard position. The starting side of an angle is always the positive x-axis.
\n" ); document.write( "The sweep that is the angle ends on a ray called the terminal side.
\n" ); document.write( "Counterclockwise turns are considered positive angles; clockwise turns are considered negative angles.
\n" ); document.write( "Angles can be measured in degrees. In trigonometry, they are often measured in radians.
\n" ); document.write( " If ray OA is turned counterclockwise until it coincides with ray OB, the angle swept can be measured as \"45%5Eo\".
\n" ); document.write( "The measure in radians is the distance traveled along the unit circle from point A to point B.
\n" ); document.write( "If ray OA is turned one whole turn counterclockwise, until it coincides with itself, the angle swept can be measured as \"360%5Eo\". In radians the measure would be \"2pi\", because the distance traveled along the circle is the whole circumference of the unit circle, whose length is \"2pi\"
\n" ); document.write( "Doing the whole turn clockwise would sweep an angle of \"-360%5Eo\" or, in radians \"-2pi\".
\n" ); document.write( "An angle of \"pi\" would correspond to half a turn counterclockwise from OA to OC, while an angle of \"-pi\" would be half a turn clockwise from OA to OC. Both angles end in the same terminal side, and are called co-terminal. An infinite number of angle are co-terminal with those two. A \"1%261%2F2\" turn counterclockwise measures \"3pi\" is also co-terminal with \"pi\" and \"-pi\", as would be a \"2%261%2F2\" clockwise turn , which would measure \"-5pi\".
\n" ); document.write( "The trigonometric functions are based on the coordinates of the point where the terminal side crosses the unit circle. For the angle AOC measuring \"-pi\" (and all the angles co-terminal with that angle) that point is C(-1,0).
\n" ); document.write( "The sine of the angle is the y-coordinate of that point, so \"sin%28-pi%29=0\".
\n" ); document.write( "The cosine of the angle is the x-coordinate of the point, so \"cos%28-pi%29=-1\".
\n" ); document.write( "It is done the same way for any angle.
\n" ); document.write( "The other trigonometric functions (tangent, cotangent, secant and cosecant) can be calculated based on the sine and cosine of the same angle.
\n" ); document.write( "\"tan%28t%29=sin%28t%29%2Fcos%28t%29\"
\n" ); document.write( "\"cot%28t%29=cos%28t%29%2Fsin%28t%29\"
\n" ); document.write( "\"sec%28t%29=1%2Fcos%28t%29\"
\n" ); document.write( "\"csc%28t%29=1%2Fsin%28t%29\"
\n" ); document.write( "For \"t=-pi\":
\n" ); document.write( "\"tan%28-pi%29=0%2F%28-1%29=0\"
\n" ); document.write( "\"cot%28-pi%29\" is undefined, because it would require dividing by \"sin%28-pi%29=0\".
\n" ); document.write( "(I suppose they want you to write IMPOSSIBLE for an answer for \"cot%28-pi%29\").
\n" ); document.write( "\"sec%28-pi%29=1%2F%28-1%29=-1\"
\n" ); document.write( "\"csc%28-pi%29\" is also undefined, because it would require dividing by \"sin%28-pi%29=0\".
\n" ); document.write( "(I suppose they want you to write IMPOSSIBLE for that one too). \n" ); document.write( "
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