VERTICAL ASYMPTOTES OF CSC SEC AND COT FUNCTIONS WORKSHEET

Problem 1 :

Let f(x) = 3 sec 2x, which of the following is the vertical asymptote on the graph f ?

a) x = π        b) x = 3π/2      c)  x = π/4      d) x = 0

Solution

Problem 2 :

Let g(x) = 4 - 2 csc (πx), which of the following is the vertical asymptote on the graph g ?

a) x = π/2        b) x = π       c)  x = 1/2      d) x = 1

Solution

Problem 3 :

Let k(x) = -5 cot (2πx), which of the following is the vertical asymptote on the graph k ?

a) x = 1/4        b) x = 1/2       c)  x = π/2      d) x = 2π

Solution

Problem 4 :

In order to graph y = (1/2) tan 2x, an interval containing one period is found by solving - π/2 < 2x < π/2.

An interval containing one period is two consecutive asymptotes occur at x = and x = .

Solution

Problem 5 :

An interval containing one period of y = tan (x - π/2) is at x = . Thus, two consecutive asymptotes occur and x = and x = 

Solution