Find the value of X if \(cos x = \frac{5}{8}for 0^o\le X\le 180^o\)

Answer Details

To find the value of X, we can use the inverse cosine function (also known as the arccosine function) on both sides of the equation: \begin{align*} \cos x &= \frac{5}{8} \\ \Rightarrow \quad x &= \cos^{-1} \left( \frac{5}{8} \right) \end{align*} Using a calculator, we can find that: \begin{align*} x &\approx 51.32^\circ \end{align*} Therefore, the correct answer is 51.3^o.