Question 769455
{{{ sin( 2x ) - cos( 2x ) = 0 }}}
{{{ sin( 2x ) = cos( 2x ) }}}
The sin and cos are equal when:
{{{ 2x = pi/4 }}}
{{{ 2x = ( 5*pi )/4 }}}
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At an angle of {{{ pi/4 }}},
{{{ sin( pi/4 ) = 1/sqrt(2) }}}
{{{ cos( pi/4 ) = 1/sqrt(2) }}}
and
{{{ sin( 5*pi/4 ) = (-1)/sqrt(2) }}}
{{{ cos( 5*pi/4 ) = (-1)/sqrt(2) }}}
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So, if I say
{{{ 2x = pi/4 }}}
{{{ x = pi/8 }}}
and
{{{ 2x = ( 5*pi )/4 }}}
{{{ x = ( 5*pi ) / 8 }}}
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Solutions for {{{ x }}} are between ( 0, 2pi ), so
{{{ 2x = 2*pi + pi/4 }}}
{{{ 2x = 2*pi + (5pi)/4 }}}
are solutions also