document.write( "Question 720779: if sinq is negative and cosq is negative in which quadrant does the terminal side q lie?\r
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Algebra.Com's Answer #441957 by Edwin McCravy(20056) $\"\"$ $\"About$

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document.write( "Remember the sentence \"ALL STUDENTS TAKE CALCULUS\" to remember the\r\n" );
document.write( "letters A,S,T,C for these words: \r\n" );
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document.write( "1. the word ALL\r\n" );
document.write( "2. the word SINE\r\n" );
document.write( "3. the word TANGENT\r\n" );
document.write( "4. the word COSINE\r\n" );
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document.write( "This works for the basic three trig functions SINE, COSINE, TANGENT.\r\n" );
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document.write( "Quadrant I:   A for ALL three of the basic three trig functions are positive\r\n" );
document.write( "              in quadrant I which is 0 < q < 90° if q is measured in degrees \r\n" );
document.write( "              or 0 < q <  if q is measured in radians.\r\n" );
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document.write( "Quadrant II:  S for the SINE is positive and the other two basic trig functions\r\n" );
document.write( "              are negative in quadrant II which is 90° < q < 180° if q is \r\n" );
document.write( "              measured in degrees or < q < p if q is measured in radians.\r\n" );
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document.write( "Quadrant III: T for the TANGENT is positive and the other two basic trig functions\r\n" );
document.write( "              are negative in quadrant III which is 180° < q < 270° if q is \r\n" );
document.write( "              measured in degrees or p < q <  if q is measured in radians.\r\n" );
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document.write( "Quadrant IV:  C for the COSINE is positive and the other two basic trig functions\r\n" );
document.write( "              are negative in quadrant IV which is 270° < q < 360° if q is \r\n" );
document.write( "              measured in degrees or < q < 2p if q is measured in radians.\r\n" );
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document.write( "The above scheme tells you what signs the three basic trig functions SINE,\r\n" );
document.write( "COSINE, and TANGENT have in the various quadrants.  It does not work for\r\n" );
document.write( "SECANT, COSECANT and COTANGENT, so don't mistake the S and C from \"ALL\r\n" );
document.write( "STUDENTS TAKE CALCULUS\" for those, but only for SINR and COSINE.  The way to\r\n" );
document.write( "remember the signs of the SECANT, COSECANT, and COTANGENT, is to remember that\r\n" );
document.write( "the SECANT is the reciprocal of the COSINE and the SECANT will have the same\r\n" );
document.write( "sign as the COSINE. The same for the other two reciprocal functions.  The\r\n" );
document.write( "COSECANT is the reciprocal of the SINE and the COSECANT will have the same\r\n" );
document.write( "sign as the SINE. The COTANGENT is the reciprocal of the TANGENT and the\r\n" );
document.write( "COTANGENT will have the same sign as the TANGENT.\r\n" );
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document.write( "Your question is:\r\n" );
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document.write( "Think of the sentence \"ALL STUDENTS TAKE CALCULUS\".  The SINE is positive\r\n" );
document.write( "in quadrants I and II and negative in quadrants III and IV.  So the answer\r\n" );
document.write( "is either quadrant III or IV.  The cosine is positive in quadrants I and IV,\r\n" );
document.write( "and negative in quadrants II and III, so that eliminates quadrant IV, and so\r\n" );
document.write( "the answer is quadrant III.\r\n" );
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document.write( "Edwin

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