solve for x in the given interval. you should be secx = - 1, 2π≤x≤3π the solution(s) is/are x = (simplify…

Explanation:

Step1: Recall secant - cosine relation

Since $\sec x=\frac{1}{\cos x}$, the equation $\sec x = - 1$ can be rewritten as $\frac{1}{\cos x}=-1$, which implies $\cos x=-1$.

Step2: Find the general solution of $\cos x=-1$

The general solution of $\cos x = - 1$ is $x=(2n + 1)\pi$, where $n\in\mathbb{Z}$.

Step3: Find the solution in the given interval

We want to find $x$ such that $2\pi\leq x\leq3\pi$. Let $2n + 1$ satisfy the condition for $x$ in the given interval. When $n = 1$, $x=(2\times1 + 1)\pi=3\pi$.

Answer:

$3\pi$