Question 195808
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*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 2\cos^2{t} - 9\cos{t} = 5]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 2\cos^2{t} - 9\cos{t} - 5 = 0]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ (2\cos{t} + 1)(cos{t} - 5) = 0]


Use the Zero Product Rule:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \cos{t} = -\frac{1}{2}]


or


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \cos{t} = 5]


But the domain of *[tex \LARGE \cos{\theta}] is *[tex \LARGE \[-1,1\]] so exclude this root.


Now all you need to do is determine:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ t = \arccos{(-\frac{1}{2})}]


John
*[tex \LARGE e^{i\pi} + 1 = 0]
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