Question 935570
Divide top and bottom by {{{ sqrt( 2 ) }}}
{{{ sqrt(2) / 2 = 1 / sqrt( 2 ) }}}
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{{{ sin( x ) = a/c }}}
label the components:
{{{ a/c = 1/sqrt(2) }}}
Find the horizontal component
{{{ b^2 = c^2 - a^2 }}}
{{{ b^2 = (sqrt(2))^2 - 1^2 }}}
{{{ b^2 = 2 - 1 }}}
{{{ b^2 = 1 }}}
{{{ b = 1 }}}
{{{ b = -1 }}}
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{{{ cos(x) = b/c }}}
{{{ cos( x ) = 1/sqrt(2) }}}
{{{ x = pi/4 }}}
and, also
{{{ cos( x ) = -1/sqrt(2) }}}
{{{ x = 3pi/4 }}}
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{{{ 2x = pi/2 }}}
and
{{{ 2x = 3pi/2 }}}
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Finally,
{{{ cos( 2x ) = 0 }}}
In both of these cases