Question 839010
Use a substitution and the quadratic formula,
{{{u=cos(theta)}}}
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{{{5u^2+u-1=0}}}
{{{u = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
{{{u = (-1 +- sqrt( 1^2-4*5*(-1) ))/(2*5) }}}
{{{u = (-1 +- sqrt( 1+20 ))/(10) }}}
{{{u = (-1 +- sqrt( 21 ))/(10) }}}
First solution:
{{{u = (-1 + sqrt( 1+20 ))/(10)= 0.3583}}}
{{{cos(theta)=0.3583}}}
{{{theta=69.0}}}
Second solution:
{{{u = (-1 - sqrt( 1+20 ))/(10)= -0.5583}}}
{{{cos(theta)=-0.5583}}}
{{{theta=123.9}}}