Question 1157544
{{{ 12*sin^2(w) + 7*cos(w) - 13 = 0 }}}
{{{ sin^2(w) = 1 - cos^2(w) }}}
{{{ 12*( 1 - cos^2(w) ) + 7*cos(w) - 13 = 0 }}}
{{{ 12 - 12*cos^2(w) + 7*cos(w) - 13 = 0 }}}
{{{ 12*cos^2(w) - 7*cos(w) + 1 = 0 }}}
Let {{{ z = cos(w) }}}
{{{ 12z^2 - 7z + 1 = 0 }}}
{{{ ( 4z - 1 )*( 3z - 1 ) = 0 }}} ( by looking at it )
{{{ 4z = 1 }}}
{{{ z = 1/4 }}}
and
{{{ 3z = 1 }}}
{{{ z = 1/3 }}}
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{{{ cos(w) = 1/4 }}}
The cosine is positive in 1st and 4th quadrants
{{{ w = arc cos( 1/4 ) }}}
{{{ w = 1.3181 }}} radians
{{{ w = 2pi - 1.3181 = 4.9651 }}} radians
and
{{{ cos(w) = 1/3 }}}
{{{ w = arc cos( 1/3 ) }}}
{{{ w = 1.2310 }}} radians
{{{ w = 2pi - 1.2310 = 5.0522 }}} radians
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check answers (4)
{{{ w = 1.3181 }}}
{{{ 12*sin^2(w) + 7*cos(w) - 13 = 0 }}}
{{{ 12*.93749 + 7*.25 - 13 = 0 }}}
{{{ 11.25 + 1.75 - 13 = 0 }}}
{{{ 13 - 13 = 0 }}}
OK
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