document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=789386>Question 789386</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I have 2 questions\"\r<BR>\n" );
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document.write( "1)Find all values of &#952; that satisfy the equation over the interval [0, 2&#960;].<BR>\n" );
document.write( "cos theta = sin theta.   Please help me solve this problem. I do not know where to begin. I looked through some notes and tried a few answers and they are not coming out correct. The question asks that I give the smaller and larger values in rad.<BR>\n" );
document.write( "2)And the second is given cos theta= 7/8. Find the other 5 trig functions of theta. I found sec theta as 8/7. but how would I use those 2 to find the other 4 functions? \r<BR>\n" );
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document.write( "Thank you for your help,\r<BR>\n" );
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document.write( "Jolene  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #478855 by </B><A HREF=/tutors/aboutme.mpl?userid=rothauserc><B>rothauserc(4718)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rothauserc><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=rothauserc><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=478855\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> note that pi in trig equals 180 degrees so problem 1 is asking for all values from 0 to 360 degrees where cos theta = sin theta which covers all four quadrants<BR>\n" );
document.write( "1)  here we go   :-)<BR>\n" );
document.write( "cos theta = sin theta implies cos theta equals cos (pi/2 - theta), this implies that theta = 2n*pi + (pi/2 - theta) where n is 0, 1, 2, 3, 4, ....., so 2*theta = 2n*pi +pi/2 implies theta = n*pi + pi/4 , which satisfies the relation<BR>\n" );
document.write( "we see that cos theta = sin theta for theta = 45 or 225 degrees<BR>\n" );
document.write( "now convert these angles to radians by multiplying degrees by pi/180<BR>\n" );
document.write( "therefore we have pi/4 and 5*pi/4<BR>\n" );
document.write( "2)we are given cos theta = 7/8<BR>\n" );
document.write( "using the relation a^2 + b^2 = c^2 we get<BR>\n" );
document.write( "a^2 + 7^2 = 8^2<BR>\n" );
document.write( "a^2 = 64 -49 = 15<BR>\n" );
document.write( "a = 3.8<BR>\n" );
document.write( "from this we have<BR>\n" );
document.write( "sin = 3.8 / 8<BR>\n" );
document.write( "cos = 7 / 8<BR>\n" );
document.write( "tan = 3.8 / 7<BR>\n" );
document.write( "csc = 8 / 3.8<BR>\n" );
document.write( "sec = 8 / 7<BR>\n" );
document.write( "cot = 7 / 3.8\r<BR>\n" );
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