document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1151678>Question 1151678</A>: <I><SPAN STYLE=\"word-break: break-all;\"> One solution to the equation (-4/5) = sin(x) is approx -53.130<BR>\n" );
document.write( "What is the NEXT real solution to the right?<BR>\n" );
document.write( "A) x=180 + |-53.130|<BR>\n" );
document.write( "B) x=-233.13<BR>\n" );
document.write( "C) x=-53.130 + 180<BR>\n" );
document.write( "D) x=360 + (-53.130)<BR>\n" );
document.write( "E) none of these </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #773502 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=773502\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> sine is negative in the third and fourth quadrant.<BR>\n" );
document.write( "if sin(x) = -4/5, then x = -53.13010235 degrees.<BR>\n" );
document.write( "that's in the fourth quadrant.<BR>\n" );
document.write( "the equivalent angle in the first quadrant would be 360 - 306.8698976 = 53.13010235 degrees.<BR>\n" );
document.write( "the equivalent angle in the third quadrant would be 180 + 53.13010235 = 233.13010235 degrees.<BR>\n" );
document.write( "that would be 180 + absolute value of (-53.130) degrees.<BR>\n" );
document.write( "to see if is the next solution to the right, graph the equation of y = sin(x).<BR>\n" );
document.write( "here's what it looks like.<BR>\n" );
document.write( "-53 is in the fourth quadrant.<BR>\n" );
document.write( "going to the right, the next angle with sine of -4/5 is in the third quadrant of the next full 360 degree cycle.\r<BR>\n" );
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document.write( "you can see that the next angle to the right of -53.13... that has a sine of -4/5 is 233.13... degrees.\r<BR>\n" );
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document.write( "i always get the equivalent angle in the first quadrant.<BR>\n" );
document.write( "that's called the reference angle.<BR>\n" );
document.write( "from the first quadrant, it's easiest to go to any other quadrant you want.<BR>\n" );
document.write( "second quadrant angle is 180 minus the reference angle.<BR>\n" );
document.write( "third quadrant angle is 180 plus the reference angle.<BR>\n" );
document.write( "fourth quadrant angle is 360 minus the reference angle.<BR>\n" );
document.write( "those would all be positive angles.<BR>\n" );
document.write( "equivalent negative angles would be those angles minus 360 degrees. </SPAN>\n" );
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