document.write( "Question 1097963: Is sec theta = 12/5 with theta in Quadrant IV, find tan theta. \n" ); document.write( "

Algebra.Com's Answer #712349 by KMST(5328) $\"\"$ $\"About$

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In quadrant IV, cosine (and secant) are positive,
\n" ); document.write( "but,since,and tangent are negative.
\n" ); document.write( " $\"sec%28theta%29=1%2Fcos%28theta%29=12%2F5\"$ ---> $\"cos%28theta%29=5%2F12\"$
\n" ); document.write( "For all angles, $\"cos%5E2%28theta%29%2Bsin%5E2%28theta%29=1\"$ ,
\n" ); document.write( "so $\"%285%2F12%29%5E2%2Bsin%5E2%28theta%29=1\"$ --> $\"25%2F144%2Bsin%5E2%28theta%29=1\"$ --> $\"sin%5E2%28theta%29=1-25%2F144=%28144-25%29%2F144=119%2F144\"$ ,
\n" ); document.write( "and because $\"sin%28theta%29\"$ is a negative number in quadrant IV,
\n" ); document.write( " $\"sin%28theta%29=-sqrt%28119%2F144%29=-sqrt%28119%29%2F12\"$ .
\n" ); document.write( "Then, because for any angle $\"tan%28theta%29=sin%28theta%29%2Fcos%28theta%29\"$ ,
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