document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=420138>Question 420138</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Use the fundamental identities to find the value of the trigonometric function:\r<BR>\n" );
document.write( "\n" );
document.write( "Find sin alpha if cos alpha = 2/3 and alpha is in Quadrant IV </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #293669 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=293669\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> if alpha is in the fourth quadrant, then:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the cosine is positive.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the sine is negative.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "if the cosine of alpha = 2/3, this means that the x value of alpha is 2 and the hypotenuse of alpha is 3.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "this makes the angle equal to -48.1896851 degrees.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the sine of -48.1896851 degrees is equal to -.745355992\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "since the sine of alpha equals opposite divided by hypotenuse, and since hypotenuse equals 3, then we get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "-.745355992 = y/3\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "we multiply both sides of this equation by 3 to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "y = 3 * -.745355992 = -2.236067977\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "our angle in the fourth quadrant has an x value of 2 and a y value of -2.236067977.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the value of the hypotenuse squared is equal to x^2 + y^2 which equals 4 + 5 which equals 9.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the square root of that gets us the hypotenuse equals 3.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "a picture of your angle and the triangle we created from it is shown below:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/problems/420138.jpg\" alt = \"***** picture not found *****\" / >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the first quadrant is top right.<BR>\n" );
document.write( "the second quadrant is top left.<BR>\n" );
document.write( "the third quadrant is bottom left.<BR>\n" );
document.write( "the fourth quadrant is bottom right.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "alpha is the angle of the triangle whose vertex touches the intersection of the y axis and the x axis in the center of the graph. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );