document.write( "Question 296672: If the sine of an angle is negative, which other trigonometric functions will definitely have negative values? \n" ); document.write( "

Algebra.Com's Answer #213754 by jim_thompson5910(35256) $\"\"$ $\"About$

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If the sine of an angle is negative, then the cosine of that same angle may be negative, but it could also be positive. So let's move on.\r
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\n" ); document.write( "\n" ); document.write( "If the sine of an angle is negative, then the tangent of that angle will be negative only if the cosine of that angle is positive. So again we don't have a guarantee.\r
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\n" ); document.write( "\n" ); document.write( "If the sine of an angle is negative, then the cosecant (defined by $\"csc%28x%29=1%2Fsin%28x%29\"$ ) will definitely be negative since '1' is positive and dividing a positive by a negative will be negative.\r
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\n" ); document.write( "\n" ); document.write( "If the sine of an angle is negative, then the secant (defined by $\"sec%28x%29=1%2Fcos%28x%29\"$ ) will only be negative if the cosine of that angle is negative. So no guarantees here.\r
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\n" ); document.write( "\n" ); document.write( "Finally, if the sine of an angle is negative, then the cotangent (defined by $\"cot%28x%29=1%2Ftan%28x%29=cos%28x%29%2Fsin%28x%29\"$ ) will only be negative if the cosine of that angle is positive. So no guarantees here.\r
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\n" ); document.write( "\n" ); document.write( "So if sine of an angle is negative, then the only function that will definitely be negative as well is the cosecant function. \n" ); document.write( "

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