document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=51942>Question 51942</A>: <I><SPAN STYLE=\"word-break: break-all;\"> use the unit circle to evaluate the following. please help im lost \r<BR>\n" );
document.write( "\n" );
document.write( "sin(-3(3.14)/2)\r<BR>\n" );
document.write( "\n" );
document.write( "sin(133(3.14)/2)\r<BR>\n" );
document.write( "\n" );
document.write( "tan(-49(3.14)/2\r<BR>\n" );
document.write( "\n" );
document.write( "sec (-5(3.14)/2)\r<BR>\n" );
document.write( "\n" );
document.write( "csc(7(3.14)/2) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #34660 by </B><A HREF=/tutors/aboutme.mpl?userid=josmiceli><B>josmiceli(19441)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josmiceli><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=josmiceli><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=34660\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> These are problems about radian measure, which is just another way of<BR>\n" );
document.write( "measuring angles.<BR>\n" );
document.write( "You have to picture certain things, or you just wont get it. Get these<BR>\n" );
document.write( "mental pictures first. Forget numbers, mostly. Forget trig. Just poicture<BR>\n" );
document.write( "things in your head.<BR>\n" );
document.write( "A radius is a string fastened at one end and pulled tight. Then you<BR>\n" );
document.write( "mark a starting point on the ground where the other end is.<BR>\n" );
document.write( "You walk this string around in a circle until you come back to<BR>\n" );
document.write( "the mark you made on the ground. You just went around 360 degrees,<BR>\n" );
document.write( "and you're back where you started.<BR>\n" );
document.write( "Do you recall the formula for circumference of a circle?<BR>\n" );
document.write( "It's <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C+=+2%2Api%2Ar ALIGN=MIDDLE  ALT=\"C+=+2%2Api%2Ar\"   DISABLED_style= \"max-width:90%; height:auto;\" > where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pi ALIGN=MIDDLE  ALT=\"pi\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 3.141 and r is the radius.<BR>\n" );
document.write( "Suppose <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r+=+1 ALIGN=MIDDLE  ALT=\"r+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" > Then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C+=+2%2Api ALIGN=MIDDLE  ALT=\"C+=+2%2Api\"   DISABLED_style= \"max-width:90%; height:auto;\" >, right?<BR>\n" );
document.write( "That's what is meant by the unit circle. The radius is one.<BR>\n" );
document.write( "You just went around in a circle 360 degrees and came back to<BR>\n" );
document.write( "where you started, right? What if I call the 360 degrees by a different <BR>\n" );
document.write( "name? What if I call it <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Api ALIGN=MIDDLE  ALT=\"2%2Api\"   DISABLED_style= \"max-width:90%; height:auto;\" > RADIANS? Don't be afaid of the name.<BR>\n" );
document.write( "It's no more scary than degrees. <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Api ALIGN=MIDDLE  ALT=\"2%2Api\"   DISABLED_style= \"max-width:90%; height:auto;\" > radians for a full circle works out good because, as I<BR>\n" );
document.write( "showed you, with a radius = 1, the circumference measures <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Api ALIGN=MIDDLE  ALT=\"2%2Api\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "You just use this instead of 360 degees.<BR>\n" );
document.write( "So what's half way around the circle?<BR>\n" );
document.write( "That's <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Api+%2F+2 ALIGN=MIDDLE  ALT=\"2%2Api+%2F+2\"   DISABLED_style= \"max-width:90%; height:auto;\" > radians = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pi ALIGN=MIDDLE  ALT=\"pi\"   DISABLED_style= \"max-width:90%; height:auto;\" > radians<BR>\n" );
document.write( "What's 1/4 of the way around the circle?<BR>\n" );
document.write( "That's half of half-way = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pi+%2F+2 ALIGN=MIDDLE  ALT=\"pi+%2F+2\"   DISABLED_style= \"max-width:90%; height:auto;\" > radians<BR>\n" );
document.write( "That's the key to all these problems. Each problem has 3.14/2 in it<BR>\n" );
document.write( "That's the same as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pi%2F2 ALIGN=MIDDLE  ALT=\"pi%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, a quarter of the way around the circle.<BR>\n" );
document.write( "(a) sin(-3(3.14)/2)<BR>\n" );
document.write( "The minus sign means go in the clockwise direction.<BR>\n" );
document.write( "Read it as \"Go clockwise three 1/4 turns of the circle from zero point<BR>\n" );
document.write( "Where do you end up?<BR>\n" );
document.write( "(b)sin(133(3.14)/2) <BR>\n" );
document.write( "\"Make 133 1/4 turns around the circle going COUNTER-clockwise from zero.\"<BR>\n" );
document.write( "The big number 133 is not the least bit scary. What happens if you make<BR>\n" );
document.write( "four 1/4 turns around the unit circle? You're back to zero. So<BR>\n" );
document.write( "divide 133 by 4. That's how many times you got back to the zero point.<BR>\n" );
document.write( "The remainder is where you end up. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=133%2F4+=+33+%2B+1%2F4 ALIGN=MIDDLE  ALT=\"133%2F4+=+33+%2B+1%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >. So,<BR>\n" );
document.write( "you're <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pi%2F2 ALIGN=MIDDLE  ALT=\"pi%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > radians from zero in the COUNTER-clockwise direction.<BR>\n" );
document.write( "(c) tan(-49(3.14)/2 <BR>\n" );
document.write( "Read like this \"Make 49 one-quarter turns in the CLOCK-WISE direction from zero.\"<BR>\n" );
document.write( "Again, divide 49 by 4 to get the number of times you go back to zero.<BR>\n" );
document.write( "The remainder is where you end up, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=49%2F4+=+12+%2B+1%2F4 ALIGN=MIDDLE  ALT=\"49%2F4+=+12+%2B+1%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "Remember, you're <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pi%2F2 ALIGN=MIDDLE  ALT=\"pi%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > radians in the clockwise direction from zero now<BR>\n" );
document.write( "----------------<BR>\n" );
document.write( "That's the hardest part. Now Use the rules of trig to solve each one.<BR>\n" );
document.write( "For example, <BR>\n" );
document.write( "(a) sin(-3(3.14)/2) What's the sin<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pi%2F2 ALIGN=MIDDLE  ALT=\"pi%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > where you ended up? It's +1<BR>\n" );
document.write( "(b) sin(133(3.14)/2) What's the sin<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pi%2F2 ALIGN=MIDDLE  ALT=\"pi%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > where you ended up? It's also +1<BR>\n" );
document.write( "Picturing the trips around the circle and getting the direction right is<BR>\n" );
document.write( "the challenge. The rest is know trig facts and applying them. <BR>\n" );
document.write( "  </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );