document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1116963>Question 1116963</A>: <I><SPAN STYLE=\"word-break: break-all;\"> if angle is in Quadrant II, express the remaining trigonometric functions in terms of sin(angle). </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #731917 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=731917\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> if your angle is in quadrant 2, then:\r<BR>\n" );
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document.write( "sine is positive.<BR>\n" );
document.write( "cosine is negative.<BR>\n" );
document.write( "tangent is negative because it is sine / cosine = positive / negative = negative.<BR>\n" );
document.write( "cosecant is reciprocal of sine, therefore also positive.<BR>\n" );
document.write( "secant is reciprocal of cosine, therefore also negative.<BR>\n" );
document.write( "cotangent is reciprocal of tangent, therefore also negative.\r<BR>\n" );
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document.write( "here's a reference on the sign of the trigonometric functions in each quadrant.\r<BR>\n" );
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document.write( "<a  rel=nofollow HREF= \"http://www.sparknotes.com/math/trigonometry/trigonometricfunctions/section3/\" target = \"_blank\">http://www.sparknotes.com/math/trigonometry/trigonometricfunctions/section3/</a>\r<BR>\n" );
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document.write( "the rules are summarized another way below:\r<BR>\n" );
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document.write( "sine is positive in first and second quadrant.<BR>\n" );
document.write( "cosine is positive in first and fourth quadrant.<BR>\n" );
document.write( "tangent is positive in first and third quadrant.\r<BR>\n" );
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document.write( "sine is negative in third and fourth quadrant.<BR>\n" );
document.write( "cosine is negative in second and third quadrant.<BR>\n" );
document.write( "tangent is negative in second and fourth quadrant.\r<BR>\n" );
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document.write( "it all has to do with the unit circle, which is used to display the angles in each quadrant and to find their associated trigonometric functions.\r<BR>\n" );
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document.write( "the radius of this unit circle is equal to 1.\r<BR>\n" );
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document.write( "the horizontal sides of the angles formed are on the x-axis.\r<BR>\n" );
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document.write( "the vertical sides of the angles formed are parallel to the y-axis.\r<BR>\n" );
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document.write( "becauwe the radius of the circle is also the hypotenuse of the triangles formed, then the length of the hypotenuse of the triangles formed is always equal to 1.\r<BR>\n" );
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document.write( "this results in the sine funtion always being equal to y and the cosine function always being equal to x.\r<BR>\n" );
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document.write( "for example:\r<BR>\n" );
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document.write( "sine of angle = y/h.<BR>\n" );
document.write( "since h = 1, then sine of angle = y.\r<BR>\n" );
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document.write( "cosine of angle = x/h.<BR>\n" );
document.write( "since h = 1, then cosine of angle = x.\r<BR>\n" );
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document.write( "the sine function is positive when y is positive which is when y is above the x-axis.\r<BR>\n" );
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document.write( "the cosine function is positive when x is positive which is when x is to the right of the y-axis.\r<BR>\n" );
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document.write( "the tangent function is positive when x and y are both positive or when x and y are both negative.\r<BR>\n" );
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document.write( "here's my picture that should help you see what i mean.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2018/051102.jpg\" alt=\"$$$\" >\r<BR>\n" );
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document.write( "h = hypotenuse<BR>\n" );
document.write( "x = side of triangle that is adjacent to the angle.<BR>\n" );
document.write( "y = side of triangle that is opposite to the angle.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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