document.write( "Question 882836: I need help on this question
\n" ); document.write( "That sin theta = -1/3 and cos<0, find all 6 trig values for theta. \n" ); document.write( "

Algebra.Com's Answer #533136 by KMST(5328) $\"\"$ $\"About$

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One of the 6 trigonometric function values, $\"highlight%28sin%28theta%29=-1%2F3%29%29\"$ , is given.
\n" ); document.write( " $\"%28cos%28theta%29%29%5E2%2B%28sin%28theta%29%29%5E2=1\"$
\n" ); document.write( " $\"%28cos%28theta%29%29%5E2%2B%28-1%2F3%29%5E2=1\"$
\n" ); document.write( " $\"%28cos%28theta%29%29%5E2%2B1%2F9=1\"$
\n" ); document.write( " $\"%28cos%28theta%29%29%5E2=1-1%2F9\"$
\n" ); document.write( " $\"%28cos%28theta%29%29%5E2=8%2F9\"$ ---> $\"system%28cos%28theta%29=sqrt%288%2F9%29%2C%22or%22%2Ccos%28theta%29=-sqrt%288%2F9%29%29\"$
\n" ); document.write( "Since $\"cos%28theta%29%3C0\"$ ,
\n" ); document.write( " $\"cos%28theta%29=-sqrt%288%2F9%29\"$ --> $\"cos%28theta%29=-sqrt%288%29%2Fsqrt%289%29\"$ --> $\"highlight%28cos%28theta%29=-2sqrt%282%29%2F3%29%29\"$
\n" ); document.write( " $\"csc%28theta%29=1%2Fsin%28theta%29\"$ --> $\"csc%28theta%29=1%2F%28-1%2F3%29\"$ --> $\"csc%28theta%29=1%2A%28-3%2F1%29\"$ --> $\"highlight%28csc%28theta%29=-3%29\"$
\n" ); document.write( " $\"sec%28theta%29=1%2Fcos%28theta%29\"$ --> $\"sec%28theta%29=1%2F%28-2sqrt%282%29%2F3%29\"$ --> $\"sec%28theta%29=-3%2F2sqrt%282%29\"$ --> $\"sec%28theta%29=-3sqrt%282%29%2F2sqrt%282%29sqrt%282%29%29\"$ --> $\"highlight%28sec%28theta%29=-3sqrt%282%29%2F4%29\"$
\n" ); document.write( " $\"tan%28theta%29=sin%28theta%29%2Fcos%28theta%29\"$
\n" ); document.write( " $\"tan%28theta%29=%28-1%2F3%29%2F%28-2sqrt%282%29%2F3%29\"$ --> $\"tan%28theta%29=%28-1%2F3%29%2A%28-3%2F2sqrt%282%29%29\"$ --> $\"tan%28theta%29=1%2F2sqrt%282%29%29\"$ --> $\"tan%28theta%29=1%2Asqrt%282%29%2F2sqrt%282%29sqrt%282%29%29\"$ --> $\"highlight%28tan%28theta%29=sqrt%282%29%2F4%29%29\"$
\n" ); document.write( " $\"cot%28theta%29=cos%28theta%29%2Fsin%28theta%29\"$
\n" ); document.write( " $\"cot%28theta%29=%28-2sqrt%282%29%2F3%29%2F%28-1%2F3%29\"$ --> $\"cot%28theta%29=%28-2sqrt%282%29%2F3%29%2A%28-3%29\"$ --> $\"highlight%28cot%28theta%29=2sqrt%282%29%29%29\"$ \n" ); document.write( "

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