document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=187426>Question 187426</A>: <I><SPAN STYLE=\"word-break: break-all;\"> #1) If tan of theta = (6/5) and cos of theta < 0, use the fundamental identities to evaluate the other five trigonometric functions of theta. \r<BR>\n" );
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document.write( "#2) use the fundamental identities to simplify csc squared if beta (1-cos squared of beta)\r<BR>\n" );
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document.write( "#3) factor and simplify. (sec \"to the power of 4\" x- tan \"to the power of 4\" x/ sec \"squared\"  x + tan \"squared\" x) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #140497 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=140497\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> #1) If tan of theta = (6/5) and cos of theta < 0, use the fundamental identities to evaluate the other five trigonometric functions of theta.<BR>\n" );
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document.write( "If tan(theta) = 6/5 and cos(theta) < 0 then y = -6 and x = -5<BR>\n" );
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document.write( "Solve for \"r\": r = sqrt(6^2+5^2) = sqrt(61)<BR>\n" );
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document.write( "sin(theta) = y/r = -6/sqrt(61)<BR>\n" );
document.write( "cos(theta) = x/r = -5/sqrt(61)<BR>\n" );
document.write( "tan(theta) = y/x = 6/5<BR>\n" );
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document.write( "The csc, sec, and cot are the inverse of sin, cos, tan<BR>\n" );
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document.write( "#2) use the fundamental identities to simplify csc squared of beta (1-cos squared of beta)<BR>\n" );
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document.write( "csc^2(1 - cos^2)\r<BR>\n" );
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document.write( "= csc^2 - (cos^2/sin^2)\r<BR>\n" );
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document.write( "= (1/sin^2) - (cos^2/sin^2)\r<BR>\n" );
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document.write( "= (1 - cos^2)/sin^2\r<BR>\n" );
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document.write( "= sin^2/sin^2\r<BR>\n" );
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document.write( "= 1<BR>\n" );
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document.write( "#3) factor and simplify. (sec \"to the power of 4\" x- tan \"to the power of 4\" x/ sec \"squared\" x + tan \"squared\" x)<BR>\n" );
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document.write( "[sec^4(x) - tan^4(x)] / [sec^2(x) + tan^2(x)]\r<BR>\n" );
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document.write( "= [(sec^2+tan^2)(sec^2-tan^2)] / [sec^2 + tan^2]\r<BR>\n" );
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document.write( "= sec^2(x) - tan^2(x) \r<BR>\n" );
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document.write( "= 1<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H. </SPAN>\n" );
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