document.write( "Question 615316: How to find the sin, cos and tan of 19pi/6 using the unit circle. \n" ); document.write( "

Algebra.Com's Answer #387084 by jsmallt9(3758) $\"\"$ $\"About$

You can put this solution on YOUR website!
Since $\"2pi+=+%2812pi%29%2F6\"$ , $\"%2819pi%29%2F6\"$ would be an $\"%287pi%29%2F6\"$ more than one full circle. So $\"%2819pi%29%2F6\"$ and $\"%287pi%29%2F6\"$ are co-terminal angles and will have the same sin, cos and tan values.

\n" ); document.write( "Since $\"pi+=+%286pi%29%2F6\"$ , $\"%287pi%29%2F6\"$ is $\"pi%2F6\"$ more than $\"pi\"$ . This makes $\"%287pi%29%2F6\"$ (and $\"%2819pi%29%2F6\"$ ) terminate in the 3rd quadrant with a reference angle of $\"pi%2F6\"$

\n" ); document.write( "Since $\"sin%28pi%2F6%29+=+1%2F2\"$ and since sin is negative in the 3rd quadrant, $\"sin%28%287pi%29%2F6%29+=+sin%28%2819pi%29%2F6%29+=+-1%2F2\"$
\n" ); document.write( "Since $\"cos%28pi%2F6%29+=+sqrt%283%29%2F2\"$ and since cos is negative in the 3rd quadrant, $\"cos%28%287pi%29%2F6%29+=+cos%28%2819pi%29%2F6%29+=+-sqrt%283%29%2F2\"$
\n" ); document.write( "Since $\"tan%28pi%2F6%29+=+%281%2F2%29%2F%28sqrt%283%29%2F2%29+=+1%2Fsqrt%283%29+=+sqrt%283%29%2F3\"$ and since tan is positive in the 3rd quadrant, $\"tan%28%287pi%29%2F6%29+=+tan%28%2819pi%29%2F6%29+=+sqrt%283%29%2F3\"$ \n" ); document.write( "

\n" );