Question

Find the exact values of x between 0 and 2pi for which: Cos x = sqrt3/2

Answer 1

Ответ:

Объяснение:

cos(x) = $\frac{\sqrt{3} }{2}$

x = ±$\frac{pi}{6}$

Answer 2

The equation you're dealing with is:

$\cos(x) = \frac{\sqrt{3}}{2}$

This equation is satisfied by angles whose cosine is equal to $\frac{\sqrt{3}}{2}$. In the interval $[0, 2\pi]$, there are two such angles: $\frac{\pi}{6}$ and $\frac{11\pi}{6}$. This is because the cosine function is positive in the first and fourth quadrants, and $\frac{\pi}{6}$ and $\frac{11\pi}{6}$ are angles where the cosine value matches $\frac{\sqrt{3}}{2}$. These angles can be expressed as follows:

$x = \frac{\pi}{6}$ $x = \frac{11\pi}{6}$

So, the exact values of $x$ between $0$ and $2\pi$ for which $\cos(x) = \frac{\sqrt{3}}{2}$ are $\frac{\pi}{6}$ and $\frac{11\pi}{6}$.