cosx=-(5)/(13),xin [(pi )/(2),pi ]

To solve the equation $\cos x = -\frac{5}{13}$ in the interval $[\frac{\pi}{2}, \pi]$, we need to find the value of $x$ that satisfies this equation.<br /><br />The cosine function is negative in the second quadrant, which corresponds to the interval $[\frac{\pi}{2}, \pi]$. Therefore, we can use the inverse cosine function to find the value of $x$.<br /><br />The inverse cosine function, denoted as $\cos^{-1}$, is defined as the angle whose cosine is a given value. In this case, we have:<br /><br />$\cos^{-1}(-\frac{5}{13})$<br /><br />Using a calculator or a trigonometric table, we can find the value of $\cos^{-1}(-\frac{5}{13})$ to be approximately $\frac{2\pi}{3}$.<br /><br />Therefore, the solution to the equation $\cos x = -\frac{5}{13}$ in the interval $[\frac{\pi}{2}, \pi]$ is:<br /><br />$x = \frac{2\pi}{3}$