document.write( "Question 169158: Name the quadrant in which the angle θ lies. cosθ<0, cscθ<0 \n" ); document.write( "

Algebra.Com's Answer #124735 by jim_thompson5910(35256) $\"\"$ $\"About$

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Remember $\"csc%28theta%29=1%2Fsin%28theta%29\"$ . So if $\"csc%28theta%29%3C0\"$ then $\"1%2Fsin%28theta%29%3C0\"$ (ie sine is negative)\r
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\n" ); document.write( "\n" ); document.write( "So if cosθ<0, then we're dealing with quadrants 2 and 3 (which are the left most quadrants). Also, since $\"1%2Fsin%28theta%29%3C0\"$ (which means that sine is negative), this means that we're dealing with the lower quadrants 3 and 4. \r
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\n" ); document.write( "\n" ); document.write( "Take the two regions and find the intersection, you'll find that the only quadrant that they have in common is quadrant 3. So angle θ lies in quadrant 3. \n" ); document.write( "

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