document.write( "Question 960796: Let t be a real number with cos(t)=3/7, 3pi/2 < t < 2pi Find the exact value for each of the following: \r
\n" ); document.write( "\n" ); document.write( "a. sin(t+3pi/2)
\n" ); document.write( "b. sec(-t)
\n" ); document.write( "c. cos(2pi)
\n" ); document.write( "d.cos(4pi/3 - t) \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Please explain what these means how these are solved I have to understand!
\n" ); document.write( "Thank you! in advance \n" ); document.write( "
Algebra.Com's Answer #587196 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
Let t be a real number with \"cos%28t%29=3%2F7\", \"3pi%2F2+%3C+t+%3C+2pi\" Find the exact value for each of the following:
\n" ); document.write( "
\r\n" );
document.write( "therefore angle t is in the 4th quadrant.\r\n" );
document.write( "

\n" ); document.write( "a. sin(t+3pi/2)
\n" ); document.write( "
\r\n" );
document.write( "Use the identity \"sin%28A%2BB%29=sin%28A%29cos%28B%29%2Bcos%28A%29sin%28B%29\"\r\n" );
document.write( "\r\n" );
document.write( "\"sin%28t%2B3pi%2F2%29\"\"%22%22=%22%22\"\"sin%28t%29cos%283pi%2F2%29%2Bcos%28t%29sin%283pi%2F2%29\"\r\n" );
document.write( "\"sin%28t%2B3pi%2F2%29\"\"%22%22=%22%22\"\"sin%28t%29%280%29%2Bcos%28t%29%28-1%29\"\r\n" );
document.write( "\"sin%28t%2B3pi%2F2%29\"\"%22%22=%22%22\"\"-cos%28t%29\"\r\n" );
document.write( "\"sin%28t%2B3pi%2F2%29\"\"%22%22=%22%22\"\"-3%2F7\"\r\n" );
document.write( "

\n" ); document.write( "b. sec(-t)
\n" ); document.write( "
\r\n" );
document.write( "Multiplying an angle by -1 moves the angle t from 4th quadrant to 1st quadrant,\r\n" );
document.write( "and the secant is the reciprocal of the cosine and is positive in 1st and 4th\r\n" );
document.write( "quadrants. So\r\n" );
document.write( "\r\n" );
document.write( "\"sec%28-t%29\"\"%22%22=%22%22\"\"sec%28t%29\"\"%22%22=%22%22\"\"1%2Fcos%28t%29\"\"%22%22=%22%22\"\"1%2F%283%2F7%29\"\"%22%22=%22%22\"\"7%2F3\"\r\n" );
document.write( "\r\n" );
document.write( "

\n" ); document.write( "c. cos(2pi)
\n" ); document.write( "
\r\n" );
document.write( "That's just 1.  It has nothing to do with t.\r\n" );
document.write( "

\n" ); document.write( "d.cos(4pi/3 - t)
\n" ); document.write( "
\r\n" );
document.write( "Use the identity \"cos%28A-B%29=cos%28A%29cos%28B%29%2Bsin%28A%29sin%28B%29\"\r\n" );
document.write( "\r\n" );
document.write( "\"cos%284pi%2F3-t%29=cos%284pi%2F3%29cos%28t%29%2Bsin%284pi%2F3%29sin%28t%29\"\r\n" );
document.write( "\"cos%284pi%2F3-t%29=%28-1%2F2%29%283%2F7%29%2B%28-sqrt%283%29%2F2%29sin%28t%29\"\r\n" );
document.write( "\"cos%284pi%2F3-t%29=%28-3%2F14%29%2B%28-sqrt%283%29%2F2%29sin%28t%29\"\r\n" );
document.write( "\r\n" );
document.write( "Use identity \"sin%28A%29=+%22%22+%2B-+sqrt%281-cos%5E2%28A%29%29\"\r\n" );
document.write( "since t is in quadrant 4 where sine is negative we use \r\n" );
document.write( "the negative:\r\n" );
document.write( "\r\n" );
document.write( "\"cos%284pi%2F3-t%29=%28-3%2F14%29%2B%28-sqrt%283%29%2F2%29%28-sqrt%281-cos%5E2%28t%29%29%29\"\r\n" );
document.write( "\"cos%284pi%2F3-t%29=%28-3%2F14%29%2B%28sqrt%283%29%2F2%29%28sqrt%281-cos%5E2%28t%29%29%29\"\r\n" );
document.write( "\"cos%284pi%2F3-t%29=%28-3%2F14%29%2B%28sqrt%283%29%2F2%29%28sqrt%281-%283%2F7%29%5E2%29%29\"\r\n" );
document.write( "\"cos%284pi%2F3-t%29=%28-3%2F14%29%2B%28sqrt%283%29%2F2%29%28sqrt%281-9%2F49%29%29\"\r\n" );
document.write( "\"cos%284pi%2F3-t%29=%28-3%2F14%29%2B%28sqrt%283%29%2F2%29%28sqrt%2849%2F49-9%2F49%29%29\"\r\n" );
document.write( "\"cos%284pi%2F3-t%29=%28-3%2F14%29%2B%28sqrt%283%29%2F2%29%28sqrt%2840%2F49%29%29\"\r\n" );
document.write( "\"cos%284pi%2F3-t%29=%28-3%2F14%29%2B%28sqrt%283%29%2F2%29%28sqrt%2840%29%2F7%29\"\r\n" );
document.write( "\"cos%284pi%2F3-t%29=%28-3%2F14%29%2B%28sqrt%283%29%2F2%29%28sqrt%284%2A10%29%2F7%29\"\r\n" );
document.write( "\"cos%284pi%2F3-t%29=%28-3%2F14%29%2B%28sqrt%283%29%2F2%29%282sqrt%2810%29%2F7%29\"\r\n" );
document.write( "\"cos%284pi%2F3-t%29=%28-3%2F14%29%2B%282sqrt%2830%29%2F14%29\"\r\n" );
document.write( "\"cos%284pi%2F3-t%29=%28-3%2B2sqrt%2830%29%29%2F14\"\r\n" );
document.write( "  \r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Edwin
\n" ); document.write( "
\n" );