document.write( "Question 903166: Use trigonometric identities to find the exact value of tan theta if sin theta=1/3 and tan theta<0 \n" ); document.write( "
Algebra.Com's Answer #547837 by Edwin McCravy(20056)\"\" \"About 
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document.write( "Since \"tan%28theta%29%3C0\" then \"theta\" is either in QII or QIV.\r\n" );
document.write( "Since \"sin%28theta%29\" is given as a positive number \"1%2F3\", then\r\n" );
document.write( "\"theta\" is in QII\r\n" );
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document.write( "So\r\n" );
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document.write( "(1)   \"tan%28theta%29=1%2F%283cos%28theta%29%29\"\r\n" );
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document.write( "But we will need \"cos%28theta%29\", which is negative in QII.\r\n" );
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document.write( "\"sin%5E2%28theta%29%2Bcos%5E2%28theta%29=1\"\r\n" );
document.write( "\"%281%2F3%29%5E2%2Bcos%5E2%28theta%29=1\"\r\n" );
document.write( "\"1%2F9%2Bcos%5E2%28theta%29=1\"\r\n" );
document.write( "\"1%2B9cos%5E2%28theta%29=9\"\r\n" );
document.write( "\"9cos%5E2%28theta%29=8\"\r\n" );
document.write( "\"cos%5E2%28theta%29=8%2F9\"\r\n" );
document.write( "\"cos%28theta%29=-sqrt%288%2F9%29\"  <-- we take the negative square root since cosine is negative in QII\r\n" );
document.write( "\"cos%28theta%29=-sqrt%288%29%2F3\"\r\n" );
document.write( "\"cos%28theta%29=-sqrt%284%2A2%29%2F3\"\r\n" );
document.write( "\"cos%28theta%29=-2sqrt%282%29%2F3\"\r\n" );
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document.write( "Now go back to equation (1)\r\n" );
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document.write( "Edwin
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