Answer:
"[tex][x|x=\frac{k}{4}\pi][/tex] for every integer [tex]k[/tex]"
Step-by-step explanation:
The function has zeroes at the x-intercepts in the graph.
If you look at the graph from 0 to [tex]\pi[/tex], you will see that the graph cuts the x-axis at 4 points.
They are at half of [tex]\frac{\pi}{2}[/tex], which is [tex]\frac{\pi}{4}[/tex], at [tex]\frac{\pi}{2}[/tex], at half point between [tex]\frac{\pi}{2}[/tex] and [tex]\pi[/tex], which is at [tex]\frac{3\pi}{4}[/tex], and at [tex]\pi[/tex].
They are basically all multiples of [tex]\frac{\pi}{4}[/tex].
Looking at the answer choices, the third choice is correct.
Plugging in k=1, k=2, k=3, and k=4 into the equation, we see that the zeroes are exactly what we saw. Also, the negative side of the function holds true as well.
Third answer choice is right.
