Solve the equation for exact solutions over the interval $[0, 2 π)$ .
$8 \tan 3 x = 8$
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. The solutionset is
(Type an exact answer, using $π$ as needed. Type your answer in radians. Use integers or
B. The solution is the empty set.

Answer

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Answer

Final Answer: The solution set is ${\frac{π}{12}, \frac{5 π}{12}, \frac{3 π}{4}, \frac{13 π}{12}, \frac{17 π}{12}, \frac{7 π}{4}}$ .

Steps

Step 1 ：The given equation is $8 \tan 3 x = 8$ .

Step 2 ：We can simplify this equation by dividing both sides by 8 to get $\tan 3 x = 1$ .

Step 3 ：The solutions to this equation are the values of $x$ for which $3 x$ is an odd multiple of $\frac{π}{4}$ in the interval $[0, 2 π)$ .

Step 4 ：We can find these values by dividing the odd multiples of $\frac{π}{4}$ by 3.

Step 5 ：The solutions to the equation are $x = \frac{π}{12}, \frac{5 π}{12}, \frac{3 π}{4}, \frac{13 π}{12}, \frac{17 π}{12}, \frac{7 π}{4}$ .

Step 6 ：These are the values of $x$ for which $\tan 3 x = 1$ in the interval $[0, 2 π)$ .

Step 7 ：Final Answer: The solution set is ${\frac{π}{12}, \frac{5 π}{12}, \frac{3 π}{4}, \frac{13 π}{12}, \frac{17 π}{12}, \frac{7 π}{4}}$ .