document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1207211>Question 1207211</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Can you please help me solve the following trigonometry exact values with working out:<BR>\n" );
document.write( "sin 2pi/3   <BR>\n" );
document.write( "cos 3pi/4<BR>\n" );
document.write( "tan 5pi/6<BR>\n" );
document.write( "sin 7pi/6<BR>\n" );
document.write( "cos 5pi/4<BR>\n" );
document.write( "tan 4pi/3<BR>\n" );
document.write( "sin 5pi/3<BR>\n" );
document.write( "cos 7pi/4<BR>\n" );
document.write( "tan 11pi/6<BR>\n" );
document.write( "I know it is a lot of questions to ask but I am quite stuck. It would be nice if all of them are complete but if this is too much to ask for atleast half to 3/4s of them would be nice. Thankyou! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #844953 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=844953\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "If you are allowed access to the Unit Circle then it's best to use it<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src = \"https://www.mathsisfun.com/geometry/images/circle-unit-radians.svg\"><BR>\n" );
document.write( "Image Source:<BR>\n" );
document.write( "https://www.mathsisfun.com/geometry/unit-circle.html\r<BR>\n" );
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document.write( "The x and y coordinates of the terminal point represent the cosine and sine values respectively.\r<BR>\n" );
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document.write( "For example, <BR>\n" );
document.write( "cos(pi/3) = 1/2<BR>\n" );
document.write( "sin(pi/3) = sqrt(3)/2<BR>\n" );
document.write( "pi/3 radians = 60 degrees\r<BR>\n" );
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document.write( "Focus on the upper right corner known as quadrant I.<BR>\n" );
document.write( "Notice 30-60-90 triangles are useful for the 30 and 60 degree angles.<BR>\n" );
document.write( "A 45-45-90 triangle is useful for the 45 degree angle. <BR>\n" );
document.write( "Use the appropriate template for each.\r<BR>\n" );
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document.write( "Once you've memorized the items in the 1st quadrant, you can then use symmetry to apply things to the other quadrants.\r<BR>\n" );
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document.write( "One last thing to note:<BR>\n" );
document.write( "tangent is the ratio sine/cosine<BR>\n" );
document.write( "So to compute something like tan(11pi/6), you'll divide the values sin(11pi/6) over cos(11pi/6).\r<BR>\n" );
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document.write( "With all that in mind you should get these answers\r<BR>\n" );
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document.write( "sin(2pi/3) = <font color=red>sqrt(3)/2</font><BR>\n" );
document.write( "cos(3pi/4) = <font color=red>-sqrt(2)/2</font><BR>\n" );
document.write( "tan(5pi/6) = <font color=red>-sqrt(3)/3</font><BR>\n" );
document.write( "sin(7pi/6) = <font color=red>-1/2</font><BR>\n" );
document.write( "cos(5pi/4) = <font color=red>-sqrt(2)/2</font>\r<BR>\n" );
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document.write( "tan(4pi/3) = <font color=red>sqrt(3)</font><BR>\n" );
document.write( "sin(5pi/3) = <font color=red>-sqrt(3)/2</font><BR>\n" );
document.write( "cos(7pi/4) = <font color=red>sqrt(2)/2</font><BR>\n" );
document.write( "tan(11pi/6) = <font color=red>-sqrt(3)/3</font>\r<BR>\n" );
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document.write( "Please let me know if you have a specific question about how to arrive at any one of these answers. \r<BR>\n" );
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document.write( "One way to verify the answers is to use WolframAlpha. GeoGebra is another useful option (you'll need to use the CAS tool). There are many other ways to verify.<BR>\n" );
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