Question

Find the first TWO non-negative asymptotes and the first negative asymptote of the graph of y in radians y=cot(x-(pi/6)). smallest non-negative asymptote: x= second non-negative asymptote: x= first negative asymptote: x= Find the first TWO non-negative asymptotes and the first negative asymptote of the graph of y in radians y=cot(x-(pi/6)). smallest non-negative asymptote: x= second non-negative asymptote: x= first negative asymptote: x=

Answer 1

the graph is moved right along the x-axis by pi/6

1st negative for cot(x) is -pi... for cot(x - pi/6) its -pi + pi/6 = -5pi/6

for cot(x) x = 0 is an asymptote for cot(x - pi/6) x = pi/6 is an asymptote

2nd non negative add pi... pi + pi/6 = 7pi/6

hope this helps

Answer 2

asymptotes, or more specifically vertical asymptotes, occur when the denominator of a function tends to zero, so lets look at the denominator of that function:
by definition: cot(u) = 1/tan(u) so with your function y = 1/tan(x-(pi/6))

to find asymptotes set the denominator to zero:
\[\tan(x- \frac{\pi}{6}) = 0\]

the solutions of that equation are where your function has asymptotes. reply if you get stuck

Answer 3

really our answers should be round the other way xD