document.write( "Question 1058525: The question I am given is \"Find all values of x in the interval [0,2pi], that satisfy sin2x=cosx\" I am having some difficulty with understanding why x=2pi/6 and x=4pi/6 are not included in the solution since these angles are reference angles of sin(pi/6) = 1/2, and therefore, should equal to 1/2. But I just computed these angles on my calculator, and they do not equal 1/2...why is that? Thank you in advance! \n" ); document.write( "

Algebra.Com's Answer #673578 by ikleyn(52790) $\"\"$ $\"About$

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\n" ); document.write( "The question I am given is \"Find all values of x in the interval [0,2pi], that satisfy sin2x=cosx\" I am having some difficulty
\n" ); document.write( "with understanding why x=2pi/6 and x=4pi/6 are not included in the solution since these angles are reference angles of sin(pi/6) = 1/2,
\n" ); document.write( "and therefore, should equal to 1/2. But I just computed these angles on my calculator, and they do not equal 1/2...why is that?
\n" ); document.write( "Thank you in advance!
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document.write( "Let us consider the angle x = , the first of the two angles you are asking for.\r\n" );
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document.write( "Notice that x =  = .\r\n" );
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document.write( "Now,  =  = .\r\n" );
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document.write( "From the other side,  =  = .\r\n" );
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document.write( "So, you see that sin(2x) =/= cos(x) in this case.\r\n" );
document.write( "Therefore,  is not included to the list of solutions.\r\n" );
document.write( "Because it IS NOT a solution.\r\n" );
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\n" ); document.write( "\n" ); document.write( "For many other similar solved problems see the lessons\r
\n" ); document.write( "\n" ); document.write( "    - Solving simple problems on trigonometric equations\r
\n" ); document.write( "\n" ); document.write( "    - Solving typical problems on trigonometric equations\r
\n" ); document.write( "\n" ); document.write( "    - Solving more complicated problems on trigonometric equations\r
\n" ); document.write( "\n" ); document.write( "    - Solving advanced problems on trigonometric equations\r
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