Question 856566
The unknown is {{{ cos(x) }}}
I could say:
{{{ z = cos(x) }}}
{{{ 4z^2 - 4z - 1 = 0 }}}
Here's the graph:
{{{ graph( 400, 400, -4, 4, -4, 4, 4x^2 - 4x - 1 ) }}}
Now I can zero in:
{{{ graph( 400, 400, -.5, 0, -.5, .5, 4x^2 - 4x - 1 ) }}}
This is between {{{ z = -.5 }}} and {{{ z = 0 }}}
It looks like {{{ z = -.2 }}}
and the other zero crossing:
{{{ graph( 400, 400, 1, 1.5, -.5, .5, 4x^2 - 4x - 1 ) }}} 
This is between {{{ z = 1 }}} and {{{ z = 1.5 }}}
It looks like {{{ z = 1.2 }}}
This is invalid since the
cosine can't exceed {{{ 1 }}}
----------------------
{{{ -.2 = cos(x) }}}
{{{ x = 1.7722 }}} radians
check:
{{{ 4z^2 - 4z - 1 = 0 }}}
{{{ 4*cos^2(x) - 4*cos(x) - 1 = 0 }}}
{{{ 4*.04002 - 4*(-.20004 ) - 1 = 0 }}}
{{{ .16002 + .80004 - 1 = 0 }}}
{{{ .960024 = 1 }}}
pretty close
Hope I got it