document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=160870>Question 160870</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0321306899/algebrahomeworkh>Basic Technical Mathematics</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> Please help me :)<BR>\n" );
document.write( "Find theta for 0 degrees less tha or equal to (<or=) theta < 360 degrees for:<BR>\n" );
document.write( "a) tan theta= 0.932, sin theta<0<BR>\n" );
document.write( "b) sin theta= -0.192, tan theta<0<BR>\n" );
document.write( "c) sec theta= 2.047, cot theta <0<BR>\n" );
document.write( "d) cot theta=-0.3256,csc theta>0\r<BR>\n" );
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document.write( "#50.page 243 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #118576 by </B><A HREF=/tutors/aboutme.mpl?userid=gonzo><B>gonzo(654)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=gonzo><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=118576\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> a.  tan theta = .932, sin theta < 0.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "in order for the tangent to be positive, the angle has to be in the first or third quadrant.<BR>\n" );
document.write( "in order for the sin to be negative, the angle has to be in the third or fourth quadrant.<BR>\n" );
document.write( "looks like the angle has to be in the third quadrant to satisfy both requirements.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "calculator gives theta = 42.984... degrees.<BR>\n" );
document.write( "adding 180 to theta puts it in the third quadrant.<BR>\n" );
document.write( "180 + theta = 222.984... degrees<BR>\n" );
document.write( "tan 222.9842... = .932<BR>\n" );
document.write( "sine 222.9842... = minus<BR>\n" );
document.write( "the answer is then 180 + theta = 180 + 42.98421048 = 222.98421048.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "b.  sin theta = -.192, tan theta < 0<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "in order for the sine to be negative, the angle must be in the third or fourth quadrant.<BR>\n" );
document.write( "in order for the tangent to be negative, the angle must be in the second or fourth quadrant.<BR>\n" );
document.write( "looks like the angle has to be in the fourth quadrant to satisfy both sin and tangent requirements.<BR>\n" );
document.write( "calculator gives theta as -11.069... degrees.<BR>\n" );
document.write( "that's in the 4th quadrant but it's not showing the angle the way we want it.<BR>\n" );
document.write( "to get it the way we want to show it, we need to add 360 degrees to it. -11.069... degrees + 360 degrees = 348.930... degrees.<BR>\n" );
document.write( "sine of 348.930... = -.192<BR>\n" );
document.write( "tangent of 348.930... is negative.<BR>\n" );
document.write( "both requirements are satisfied.<BR>\n" );
document.write( "angle is 348.930...<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "c.  secant theta = 2.047, cot theta < 0<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "secant is 1/cosine.<BR>\n" );
document.write( "in order for secant to be positive, the angle must be in the first or fourth quadrant<BR>\n" );
document.write( "cotangent is 1/cotangent.<BR>\n" );
document.write( "in order for cotangent to be negative, the angle must be in second or fourth quadrant.<BR>\n" );
document.write( "looks like the angle must be in the fourth quadrant to satisfy both secant and cotangent requirements.<BR>\n" );
document.write( "since secant is 1/cos, then cos must be 1/secant.<BR>\n" );
document.write( "since calculator only solves for cos, we work with cosine.<BR>\n" );
document.write( "secant is 2.047<BR>\n" );
document.write( "1/secant equals cosine = .4885...<BR>\n" );
document.write( "angle shows as 60.756...<BR>\n" );
document.write( "to put it in the fourth quadrant subtract it from 360.<BR>\n" );
document.write( "360 - 60.756... = 299.243...<BR>\n" );
document.write( "secant of 299.243... equals 1/cosine equals 2.047 which is accurate.<BR>\n" );
document.write( "tangent of 299.243... is negative, therefore cotangent is also negative.<BR>\n" );
document.write( "answer is 299.243 degrees.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "d.  cot theta = -0.3256, csc theta > 0<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "for the cotangent to be negative, the angle must be in the second or fourth quadrant.<BR>\n" );
document.write( "for the csc to be positive, the sin is also positive and the angle must be in the first or second quadrant.<BR>\n" );
document.write( "this makes the angle must be in the second quadrant to satisfy both.<BR>\n" );
document.write( "since cotangent is 1/tangent, we divide 1 by cotangent to get tangent.<BR>\n" );
document.write( "then we can use the calculator.<BR>\n" );
document.write( "calculator give angle as -71.964 degrees which puts it in the fourth quadrant.<BR>\n" );
document.write( "to put it in the second quadrant, add 180 to it.<BR>\n" );
document.write( "-71.964 + 180 = 108.035...<BR>\n" );
document.write( "to prove this is the right angle, get the cotangent of it.<BR>\n" );
document.write( "get the tangent and then take 1/tangent to get the cotangent.<BR>\n" );
document.write( "that calculates to be -.3256 proving the angle is correct.<BR>\n" );
document.write( "to get the cosecant, get the sine and then take 1/sine to get the cosecant.<BR>\n" );
document.write( "since the sine is positive, the cosecant is also positive.<BR>\n" );
document.write( "answer is 108.035... degrees.<BR>\n" );
document.write( "cotantent is -.3256 and cosecant is positive.<BR>\n" );
document.write( "-----\r<BR>\n" );
document.write( "<BR>\n" );
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document.write( " </SPAN>\n" );
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