Answer:
x=0 or ±2 nπ where n belongs to natural numbers.
Step-by-step explanation:
The " vertical asymptote " is a vertical line that the graph of a function approaches but never touches. To find the vertical asymptotes of a rational function we set denominator=0.
We are given function y=3 cot((1/2)x)-4
which could also be written as [tex]y=3\times\frac{cos((1/2)x)}{sin((1/2)x)} -4\\\\y=\frac{3 cos((1/2)x)-4 sin((1/2)x)}{sin((1/2)x)}[/tex]
for denominator to be equal to 0 we must have sin((1/2)x)=0
⇒ (1/2)x=0
⇒ x=0 or ±2 nπ where n belongs to natural numbers.
Hence, the vertical asymptotes of the given function is x=0 or ±2 nπ where n belongs to natural numbers.
