document.write( "Question 1103336: Solve the following equation on the interval [0, 360 degrees]:
\n" ); document.write( "sin2x=1\r
\n" ); document.write( "\n" ); document.write( "This is what I have done so far:
\n" ); document.write( "Let 2x = theta
\n" ); document.write( "sin theta = 1
\n" ); document.write( "theta = 90 degrees
\n" ); document.write( "2x = 90 --> x = 45 degrees \r
\n" ); document.write( "\n" ); document.write( "Add period to theta:
\n" ); document.write( "90 + 180 = 270 --> x = 270/2 = 135 degrees
\n" ); document.write( "270+ 90 = 450 --> x = 450/2 = 225 degrees\r
\n" ); document.write( "\n" ); document.write( "I don't understand why the answer in my book says \"x = 45 degrees, 225 degrees\". According to my work done, shouldn't x = 135 degrees as well? \r
\n" ); document.write( "\n" ); document.write( "Help with this question would be really appreciated! \n" ); document.write( "

Algebra.Com's Answer #718035 by ikleyn(52817) $\"\"$ $\"About$

You can put this solution on YOUR website!
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document.write( "sin(2x) = 1  ====>\r\n" );
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document.write( "2x = .\r\n" );
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document.write( "The last equation 2x =  has TWO solutions in the interval [0,).\r\n" );
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document.write( "One of these two solutions is   = ,  which is OBVIOUS.\r\n" );
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document.write( "The second solution  is  to add    to the first solution:\r\n" );
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document.write( "     =  = .\r\n" );
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document.write( "Why ?  - Because when you take    with   = ,\r\n" );
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document.write( "you will get   = ,\r\n" );
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document.write( "which is GEOMETRICALLY THE SAME AS the ANGLE .\r\n" );
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document.write( "So your    is geometrically the same    and satisfies the original equation  sin(2x) = 1.\r\n" );
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document.write( "Notice that both   =   and   =  belong to the interval [0,), so they both are the solutions \r\n" );
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document.write( "to your original equation  sin(2x) = 1  in this interval.\r\n" );
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document.write( "The plot below confirms my arguments:\r\n" );
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document.write( "Plot y = sin(2x)  (red)  and  y = 1 (green)\r\n" );
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\n" ); document.write( "Do you understand this explanation ?\r
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\n" ); document.write( "\n" ); document.write( "If \"NO\", send a message to me through the \"Thank you\" window/form.\r
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\n" ); document.write( "\n" ); document.write( "If \"YES\", send a message to me through the \"Thank you\" window/form, and then I will explain more to you related to this kind of equations.\r
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