document.write( "Question 387952: What is the exact value of tan(cos^-1(-4/7)) ? \n" ); document.write( "

Algebra.Com's Answer #274252 by robertb(5830) $\"\"$ $\"About$

You can put this solution on YOUR website!
Let $\"alpha+=+cos%5E%28-1%29%28-4%2F7%29\"$ . Then $\"cos%28alpha%29+=+-4%2F7\"$ , and we have to find the value of $\"tan%28alpha%29\"$ . Now $\"cos%28alpha%29+=+-4%2F7\"$ ----> $\"sec%28alpha%29+=+-7%2F4\"$ , so that, by using the identity $\"%28sec%28alpha%29%29%5E2+=+1+%2B+%28tan%28alpha%29%29%5E2\"$ , we get $\"49%2F16+=+1+%2B++%28tan%28alpha%29%29%5E2\"$ , or $\"33%2F16+=+%28tan%28alpha%29%29%5E2\"$ .
\n" ); document.write( "Then $\"tan%28alpha%29+=+-sqrt%2833%29%2F4\"$ . Tangent of $\"alpha\"$ is negative because $\"cos%5E%28-1%29%28-4%2F7%29\"$ means $\"alpha\"$ is in the 2nd quadrant. \n" ); document.write( "

\n" );