Question

solve for 0<θ<2(3.14[pi]): 9cos^((2))θ-2cosθ-3=0 give answer in terms of 3.14[pi]

Answer 1

Since it can't be factored, you need to use the quadratic formula.
\[\cos(\theta)=\frac{-b \pm \sqrt{b^2-4ac}}{2a}\]
\[\cos(\theta)=\frac{-(-2) \pm \sqrt{(-2)^2-4(9)(-3)}}{2(9)}\]
\[\cos(\theta)=\frac{2 \pm \sqrt{112}}{18}\]
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\[\cos(\theta)=\frac{2 + \sqrt{112}}{18}~~~\text{and}~~~\cos(\theta)=\frac{2 - \sqrt{112}}{18}\]
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Take the inverse of both trigo and get \(\theta\)

Answer 2

You'll need this too