Use the graph of the function to answer each question. (−2π ≤ x ≤ 2π)
f(x) = cot(x)

answer:

  (a) dne

  (b) dne

  (c) increasing: (-3π/2, -π), (-π, -π/2), (π/2, π), (π, 3π/2)

      decreasing: (-2π,-3π/2), (-π/2, 0), (0, π/2), (3π/2, 2π)

  (d) minima: (-3π/2, 1), (-π/2, 1)

        maxima: (-π/2, -1), (3π/2, -1)

  (e) -2π, -π, 0, π, 2π

step-by-step explanation:

each of these questions requires you to read the graph.

(a, b) the curves do not touch the x- or y-axes, so there are no intercepts.

(d) "decreasing" means the curve goes downward from left to right. "increasing" means the curve goes upward from left to right. each of the lobes has both increasing and decreasing sections. at the asymptotes and at the relative extreme, the function is neither increasing nor decreasing, so those x-values are left off the lists.

(e) the vertical asymptotes are the x-values where the graph heads off toward ±infinity.

10000000000000000000000000000000

hope it you

step-by-step explanation:

sin(7pi/6 - pi/3)  

= sin(7pi/6 - 2pi/6)  

= sin(5pi/6)  

= sin(pi - pi/6)  

= sin(pi/6)  

= 1/2  

sin 7pi/6 - sin pi/3  

= sin (pi + pi/6) - sin pi/3  

= -sin pi/6 - sin pi/3  

= -1/2 - sqrt(3)/2  

= -(1+sqrt(3))2