document.write( "Question 1004805: Please help! I have already done most of the work.\r
\n" ); document.write( "\n" ); document.write( "Recently I asked about finding all real numbers in the interval [0, 2pi] that satisfy the equation.
\n" ); document.write( "I have worked through the problem but I feel like I have gotten stuck in some places. Here's the problem and where I'm at. Thank you in advance for your help!\r
\n" ); document.write( "\n" ); document.write( " $\"+3+sec%5E2x+tanx+=+4+tanx+\"$
\n" ); document.write( "= $\"+tanx+%283+sec%5E2x+-+4%29+\"$
\n" ); document.write( "= $\"+tanx+=+0+\"$ and $\"+3+sec%5E2x+-+4%29+=+0+\"$ .\r
\n" ); document.write( "\n" ); document.write( "Starting first with $\"+tanx+=+0+\"$ .
\n" ); document.write( "= $\"+x+=+tan%5E-1+%280%29+\"$
\n" ); document.write( "= $\"+x+=+0+\"$
\n" ); document.write( "Now, I've seen other examples that use $\"+tanx+=+0+\"$ and have the results be 0, as well as $\"+%28pi%29+\"$ and $\"+2%28pi%29+\"$ ...but I'm not quite sure why those last two should or shouldn't be included...why not $\"+%28pi%29+%2F+2+\"$ or $\"+3+%28pi%29+%2F+2+\"$ ? If you divide their sin by their cosine, doesn't it equal zero? So why choose $\"+%28pi%29+\"$ and $\"+2%28pi%29+\"$ with the zero and not others? Should I just leave it at 0, or should I include $\"+%28pi%29+\"$ and $\"+2%28pi%29+\"$ ?\r
\n" ); document.write( "\n" ); document.write( "Moving on to $\"+3+sec%5E2x+-+4%29+=+0+\"$ .
\n" ); document.write( "= $\"+%283+sec%5E2x%29+=+4+\"$
\n" ); document.write( "= $\"+%28+sec%5E2+%28x%29%29+=+%284+%2F+3%29+\"$
\n" ); document.write( "= $\"+secx+=+sqrt%284+%2F+3%29+\"$
\n" ); document.write( "= $\"+secx+=+sqrt%2812%29+%2F+3+\"$
\n" ); document.write( "= $\"+x+=+sec%5E-1+%28sqrt%2812%29+%2F+3%29+\"$
\n" ); document.write( "But now where do I go? Not quite sure how to find the arcsecant of something with a square root...How do I type that into my calculator? (I dont have a graphing calculator...but I can do sines, cosines and tangents with their inverses).\r
\n" ); document.write( "\n" ); document.write( "Help would be greatly appreciated. Thank you! :) \n" ); document.write( "

Algebra.Com's Answer #621169 by ikleyn(52781) $\"\"$ $\"About$

You can put this solution on YOUR website!
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document.write( "1.  Regarding first part of your question.\r\n" );
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document.write( "You got \r\n" );
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document.write( "tan(x) = 0. \r\n" );
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document.write( "The solutions of this equation are  x = 0, +/-, +/-, +/- , . . . , +/-, . . . .\r\n" );
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document.write( "Of them,  only 0,  and   belong to the segment  [, ]  that you pointed.\r\n" );
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document.write( "Other values that you are asking about,  like , ,  are not the roots of the equation  tan(x) = 0.\r\n" );
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document.write( "2.  Moving on to   -  = .\r\n" );
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document.write( "It is   = +/-,     or      = +/-     or     cos(x) = +/-.\r\n" );
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document.write( "If  cos(x) = ,  then x =  and x =  =  are the solutions in the segment  [, ].\r\n" );
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document.write( "If  cos(x) = -,  then x =  and x =  =  are the solutions in the segment  [, ].\r\n" );
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document.write( "I recommend you to make a sketch of the unit circle, to mark the angles 0°, 30°, 45°, 60° and 90° in it and to write \r\n" );
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document.write( "the values of sin, cos and tan for these angles.\r\n" );
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document.write( "Then mark all other angles like 120°, 135°, 150°, 180° and so on till 360° and do the same.\r\n" );
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document.write( "After that you will be much more confident in such problems.\r\n" );
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