Explanation:
Use the identity [tex]\sin{\theta} = 1 - \cos^2{\theta}[/tex] so we can write our equation as
[tex]6(1 - \cos^2{\theta}) - \cos{\theta} - 5 = 0[/tex]
or
[tex]6\cos^2{\theta} + \cos{\theta} - 1 = 0[/tex]
Let [tex]x = \cos{\theta}[/tex] so our equation becomes
[tex]6x^2 + x - 1 = 0[/tex]
Using the quadratic equation, we find that its roots are
[tex]x = \dfrac{-1 \pm \sqrt{(1)^2 - 4(6)(-1)}}{2(6)} = \dfrac{1}{3},\:-\dfrac{1}{2}[/tex]
which gives us
[tex]\cos{\theta} = \dfrac{1}{3} \Rightarrow \theta = 70.53°[/tex]
[tex]\cos{\theta} = -\dfrac{1}{2} \Rightarrow \theta = 120°[/tex]
