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what is 6cos square theta+cos theta -2=0 what the theta in degrees

Sagot :

Answer:[tex]\begin{gathered} \theta=60^o \\ OR \\ \theta=131.8^o \end{gathered}[/tex]

Explanation:

Given:

[tex]6\cos^2\theta+\cos\theta-2=0[/tex]

Let

[tex]\cos\theta=t[/tex]

Then

[tex]\begin{gathered} 6t^2+t-2=0 \\ (2t-1)(3t+2)=0 \\ 2t-1=0 \\ \Rightarrow t=\frac{1}{2} \\ \\ 3t+2=0 \\ \Rightarrow t=-\frac{2}{3} \end{gathered}[/tex]

Therefore:

[tex]\begin{gathered} \cos\theta=\frac{1}{2} \\ \\ \Rightarrow\theta=60^o \\ \\ \cos\theta=-\frac{2}{3} \\ \Rightarrow\theta=131.8^o \end{gathered}[/tex]

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