document.write( "Question 1156790: How do you figure out which quadrant the terminal side of each angle lies in based on if sin/cos/tan, etc. is greater than or less than theta?\r
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Algebra.Com's Answer #779581 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "Learn the sentence:  \"All Students Take Calculus\" to remember \"All S T C\"\r\n" );
document.write( "For the quadrants, think of this as though it were an x,y coordinate system:\r\n" );
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document.write( "                    S|A\r\n" );
document.write( "                    T|C\r\n" );
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document.write( "The major three trig functions are Sine, Cosine, and Tangent, the others\r\n" );
document.write( "are their reciprocals.  This memory device only works with the major three\r\n" );
document.write( "trig functions, Sine, Cosine and Tangent.\r\n" );
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document.write( "\"All\" reminds us that ALL trig functions are POSITIVE in the first quadrant QI.\r\n" );
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document.write( "\"STUDENTS\" reminds us that of the major three trig functions, the SINE is\r\n" );
document.write( "POSITIVE in the second quadrant QII, and the other two major trig functions are\r\n" );
document.write( "NEGATIVE there.\r\n" );
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document.write( "\"TAKE\" reminds us that of the major three trig functions, the TANGENT is\r\n" );
document.write( "POSITIVE in the third quadrant QIII, and the other two major trig functions are\r\n" );
document.write( "NEGATIVE there.\r\n" );
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document.write( "\"CALCULUS\" reminds us that of the major three trig functions, the COSINE is\r\n" );
document.write( "POSITIVE in the fourth quadrant QIV, and the other two major trig functions are\r\n" );
document.write( "NEGATIVE there.\r\n" );
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document.write( "If the major trig function, the SINE, is positive or negative in a quadrant, its\r\n" );
document.write( "reciprocal, the COSECANT is also positive or negative there.\r\n" );
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document.write( "If the major trig function, the COSINE, is positive or negative in a quadrant,\r\n" );
document.write( "its reciprocal, the SECANT is also positive or negative there.\r\n" );
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document.write( "If the major trig function, the TANGENT, is positive or negative in a quadrant,\r\n" );
document.write( "its reciprocal, the COTANGENT is also positive or negative there.\r\n" );
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document.write( "Now if we have learned that, let's go through what this information tells us:\r\n" );
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document.write( "Sec(theta)=13/12, sin(theta)<0\r\n" );
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document.write( "13/12 is a POSITIVE number, and the SECANT is not one of the major trig\r\n" );
document.write( "functions.  However we know that SECANT is the reciprocal of the major trig\r\n" );
document.write( "function, the COSINE and \"COSINE\" begins with \"C\" and so does \"Calculus\".  That\r\n" );
document.write( "tells us that theta is either in QI or QIV because those are the only two\r\n" );
document.write( "quadrants that the COSINE is POSITIVE in.\r\n" );
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document.write( "The next one, \"sin(theta)<0\", tells us that the SINE is NEGATIVE, and the SINE\r\n" );
document.write( "is NEGATIVE in QII and QIV.  So now we know that theta is in QIV.\r\n" );
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document.write( "So we draw an angle θ with its terminal side in QIV, and indicate its counter-\r\n" );
document.write( "clockwise rotation from the right side of the x-axis around to its terminal side\r\n" );
document.write( "in QIV by a red arrow:\r\n" );
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document.write( "Draw a vertical line from the end of the terminal side to the x-axis:\r\n" );
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document.write( "Now we know that the SECANT is HYPOTENUSE/ADJACENT because it's the reciprocal\r\n" );
document.write( "of the COSINE which in ADJACENT/HYPOTENUSE, so we put the numerator of 13/12,\r\n" );
document.write( "which is 13 on the HYPOTENUSE, which is denoted by the letter \"r\" and we put\r\n" );
document.write( "the denominator of 13/12, which is 12, on the ADJACENT side, which is denoted by\r\n" );
document.write( "the letter \"x\". The horizontal value of y will need to be calculated.\r\n" );
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document.write( "Next we need to calculate the OPPOSITE side or the y-value.  We use the\r\n" );
document.write( "Pythagorean theorem:\r\n" );
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document.write( "We take the negative sign because y goes down from the x-axis. So y=-5.\r\n" );
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document.write( "Now we can find any of the trig functions:\r\n" );
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document.write( "Edwin
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