solve for exact solutions over the interval 0,2π).\ncos 2x = -1\nselect the correct choice below and, if…

solve for exact solutions over the interval 0,2π).\ncos 2x = -1\nselect the correct choice below and, if necessary, fill in the answer box to complete your choice\na. the solution set is\n(simplify your answer. type an exact answer, using π as needed. use integers or fractions for any numbers in the expression. use a comma to separate answers as needed.)\nb. the solution set is ∅.

solve for exact solutions over the interval 0,2π).\ncos 2x = -1\nselect the correct choice below and, if necessary, fill in the answer box to complete your choice\na. the solution set is\n(simplify your answer. type an exact answer, using π as needed. use integers or fractions for any numbers in the expression. use a comma to separate answers as needed.)\nb. the solution set is ∅.

Answer

Explanation:

Step1: Solve for (2x)

We know that (\cos\theta=-1) when (\theta=(2k + 1)\pi), (k\in\mathbb{Z}). For (\cos2x=-1), we have (2x=(2k + 1)\pi), (k\in\mathbb{Z}).

Step2: Solve for (x)

Divide both sides of (2x=(2k + 1)\pi) by (2), we get (x=\frac{(2k + 1)\pi}{2}), (k\in\mathbb{Z}).

Step3: Find solutions in the interval ([0,2\pi))

When (k = 0), (x=\frac{\pi}{2}); when (k = 1), (x=\frac{3\pi}{2}).

Answer:

The solution set is (\frac{\pi}{2},\frac{3\pi}{2})