Question

solve the equation for exact solutions over the interval 0,2π).
4 csc 2x/9 = 2
select the correct choice below and, if necessary, fill in the answer box to complete your choice.
a. the solution set is {}.
(type an exact answer, using π as needed. type your answer in radians. use integers or fractions for any numbers in the expression. use a comma to separate answers as needed.)
b. the solution is the empty set.

Explanation:

Step1: Simplify the equation

Given \(4\csc\frac{2}{9}x = 2\). First, divide both sides by \(4\): \(\csc\frac{2}{9}x=\frac{2}{4}=\frac{1}{2}\). Since \(\csc\theta=\frac{1}{\sin\theta}\), then \(\sin\frac{2}{9}x = 2\). But the range of the sine function is \([- 1,1]\), and \(2
otin[-1,1]\).

Answer:

B. The solution is the empty set.