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cos x=-(1)/(2)

$\cos x=-\frac{1}{2}$

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Evaluate integers raised to rational exponents

Full solution

Q.

\cos x=-\frac{1}{2}

Identify angle with cosine: Identify the angle whose cosine is $-\frac{1}{2}$ . Using trigonometric identities or a unit circle, we know $\cos(120°) = -\frac{1}{2}$ and $\cos(240°) = -\frac{1}{2}$ .
Convert angles to radians: Convert the angles to radians because most mathematical problems require answers in radians. $\newline$ $120° = 120 \times (\pi/180) = 2\pi/3$ radians, $\newline$ $240° = 240 \times (\pi/180) = 4\pi/3$ radians.
Consider periodic nature: Consider the periodic nature of the cosine function. Cosine has a period of $2\pi$ , so the general solutions are: $x = \frac{2\pi}{3} + 2\pi k$ and $x = \frac{4\pi}{3} + 2\pi k$ , where $k$ is any integer.

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