document.write( "Question 3656: Which of the following trigonometric functions of x is not correct given that sin x > 0 and sec x = -2?
\n" ); document.write( "• csc x = ( 2 sq rt 3) / 3
\n" ); document.write( "• cos x = - 1 / 2
\n" ); document.write( "• cot x = - ( sq rt 3 ) / 3
\n" ); document.write( "• tan x = - ( sq rt 3 ) / 2 \n" ); document.write( "

Algebra.Com's Answer #1615 by Zenock(15) $\"\"$ $\"About$

You can put this solution on YOUR website!
I'm not sure why this is under \"Quadratic Equations\" but oh well here we go.\r
\n" ); document.write( "\n" ); document.write( "First let's define the following in terms of sin(x) and cos(x):\r
\n" ); document.write( "\n" ); document.write( " $\"+csc%28x%29=1%2Fsin%28x%29\"$ so $\"sin%28x%29=1%2Fcsc%28x%29\"$
\n" ); document.write( " $\"+sec%28x%29=1%2Fcos%28x%29+\"$ so $\"cos%28x%29=1%2Fsec%28x%29\"$
\n" ); document.write( " $\"+tan%28x%29=sin%28x%29%2Fcos%28x%29+\"$
\n" ); document.write( " $\"+cot%28x%29=1%2Ftan%28x%29=cos%28x%29%2Fsin%28x%29\"$ \r
\n" ); document.write( "\n" ); document.write( "Additionally we need to note that:
\n" ); document.write( " $\"+sin%5E2++%28x%29+%2B+cos%5E2%28x%29=1+\"$ \r
\n" ); document.write( "\n" ); document.write( "Now we begin.
\n" ); document.write( "First lets find the cos(x):
\n" ); document.write( " $\"cos%28x%29=1%2Fsec%28x%29=1%2F-2=-+1%2F2\"$ so cos x = - 1 / 2 is correct
\n" ); document.write( "Now lets find the sin(x) (Not in our list but needed):
\n" ); document.write( " $\"sin%5E2%28x%29%2Bcos%5E2%28x%29=1\"$ so $\"sin%5E2%28x%29%2B+1%2F4=1\"$ so $\"sin%5E2%28x%29=3%2F4\"$
\n" ); document.write( "Therefore: $\"+sin%28x%29+=+-sqrt%283%29%2F2+\"$ or $\"+sin%28x%29+=+sqrt%283%29%2F2+\"$
\n" ); document.write( "However from the orginal problem: $\"sin%28x%29%3E0\"$ so $\"+sin%28x%29+=+sqrt%283%29%2F2+\"$ \r
\n" ); document.write( "\n" ); document.write( "Using this information:
\n" ); document.write( " $\"csc%28x%29=1%2Fsin%28x%29=1%2F%28sqrt%283%29%2F2%29=2%2Fsqrt%283%29=2sqrt%283%29%2F3\"$ so csc x = ( 2 sq rt 3) / 3 is correct
\n" ); document.write( "

so cot x = - ( sq rt 3 ) / 3 is correct
\n" ); document.write( " $\"tan%28x%29=sin%28x%29%2Fcos%28x%29=%28sqrt%283%29%2F2%29%2F%28-+1%2F2%29=-sqrt%283%29\"$ so tan x = - ( sq rt 3 ) / 2 is **** not correct **** \n" ); document.write( "

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