document.write( "Question 1158051: if sec(t) = -5 and the terminal point of t is in quadrant iii, use the identity sin^2(t/2)=1-cos(t)/2 to find the exact value of (sin(t/2)+cos(t)) \n" ); document.write( "

Algebra.Com's Answer #854565 by KMST(5377) $\"\"$ $\"About$

You can put this solution on YOUR website!
I expect the identity was meant to be $\"sin%5E2%28t%2F2%29=%281-cos%28t%29%29%2F2\"$ .
\n" ); document.write( "What was written in the question was $\"sin%5E2%28t%2F2%29=1-cos%28t%29%2F2\"$ , which is not an identity.
\n" ); document.write( "IMPORTANT NOTE:
\n" ); document.write( "On paper, you can draw a long horizontal line under $\"1-cos%28t%29\"$ and write a $\"2\"$ under that line.
\n" ); document.write( "That long horizontal line implies invisible brackets wrapping together what is above the line,
\n" ); document.write( "and wrapping together what is below. Everyone understands that.
\n" ); document.write( "When typing, or entering formulas and numbers into a calculator, those brackets need to be typed in or keyed in.
\n" ); document.write( "If you want to calculate $\"%28101-2%29%2F%28101-1%29=99%2F100=0.99\"$ ,
\n" ); document.write( "and key in \"101-2/101-1\" into a calculators you would most likely get as a result
\n" ); document.write( " $\"101-2%2F101-1=101-1-2%2F101=100-2%2F101=%2299.980198019801...%22\"$ , which is not what you would expect.
\n" ); document.write( "I was not expecting anything, you are outsourcing problem solving to a gadget that does not understand what you want, and does just what you asked.
\n" ); document.write( "
\n" ); document.write( "BACK TO THE QUESTION:
\n" ); document.write( "Quadrant III means $\"270%5Eo%3Ct%3C180%5Eo\"$ , so that $\"135%5Eo%3Ct%2F2%3C90%5Eo\"$ .
\n" ); document.write( "That means the terminal side of angle $\"t%2F2\"$ is in quadrant II,
\n" ); document.write( "and $\"sin%28t%2F2%29%3E0\"$ .
\n" ); document.write( " $\"sec%28t%29=1%2Fcos%28t%29\"$ is another trigonometric identity,
\n" ); document.write( "and from $\"sec%28t%29=-5\"$ , we know that $\"1%2Fcos%28t%29=-5\"$ --> $\"highlight%28cos%28t%29=-1%2F5%29\"$
\n" ); document.write( "Substituting $\"-1%2F5\"$ for $\"cos%28t%29\"$ in the identity $\"sin%5E2%28t%2F2%29=%281-cos%28t%29%29%2F2\"$ , we get
\n" ); document.write( " $\"sin%5E2%28t%2F2%29\"$ $\"%22=%22\"$ $\"%281-%28-1%2F5%29%29%2F2\"$ --> $\"sin%5E2%28t%2F2%29%29\"$ $\"%22=%22\"$ $\"%281%2B1%2F5%29%2F2\"$ --> $\"sin%5E2%28t%2F2%29%29\"$ $\"%22=%22\"$ $\"%286%2F5%29%2F2\"$ --> $\"sin%5E2%28t%2F2%29%29\"$ $\"%22=%22\"$ $\"6%2F10\"$ --> $\"sin%5E2%28t%2F2%29%29\"$ $\"%22=%22\"$ $\"3%2F5\"$ --> $\"highlight%28sin%28t%2F2%29=sqrt%283%2F5%29=sqrt%2815%29%2F5%29\"$
\n" ); document.write( "Then, $\"highlight%28sin%28t%2F2%29%2Bcos%28t%29=%28sqrt%2815%29-1%29%2F5%29\"$ \n" ); document.write( "

\n" );