document.write( "Question 816119: solve tanx- 1=0 for all values of x. \n" ); document.write( "

Algebra.Com's Answer #491399 by jsmallt9(3758) $\"\"$ $\"About$

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tan(x) - 1 = 0
\n" ); document.write( "Add 1:
\n" ); document.write( "tab(x) = 1
\n" ); document.write( "We should recognize that 1 is a special angle value for tan. It tells us that the reference angle is $\"pi%2F4\"$ . Since the 1 is positive and since tan is positive in the 1st and 3rd quadrants, we should get the following general solution equations:
\n" ); document.write( " $\"x+=+pi%2F4%2B2pi%2An\"$ (for the 1st quadrant)
\n" ); document.write( " $\"x+=+pi%2Bpi%2F4%2B2pi%2An\"$ (for the 3rd quadrant)
\n" ); document.write( "The second equation simplifies:
\n" ); document.write( " $\"x+=+5pi%2F4%2B2pi%2An\"$

\n" ); document.write( "Since the problem asks for all values of x, the general solution is the answer:
\n" ); document.write( " $\"x+=+pi%2F4%2B2pi%2An\"$
\n" ); document.write( " $\"x+=+5pi%2F4%2B2pi%2An\"$

\n" ); document.write( "P.S. Since the period of tan (and cot) is $\"pi\"$ . The general solution can be expressed in a single equation:
\n" ); document.write( " $\"x+=+pi%2F4%2Bpi%2An\"$
\n" ); document.write( "(Note that the \"2\" is gone.) \n" ); document.write( "

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