Question

Sketch the graphs of the function: f(x) = 2 cosec πx

Answer 1

As we know that f (x) = cosec x is a periodic function with period 2π.

Therefore, f (x) = 2 cosec (πx) is a periodic function with period 2. Therefore, we will draw the graph of f (x) = 2 cosec (πx) in the interval [0, 2]. The values of f (x) = 2 cosec (πx) at various points in [0, 2] are listed in the following table:

x	0 (A)	1/2 (B)	1 (C)	-1 (D)	3/2 (E)	-2 (F)	2 (G)	5/2 (H)
f (x) = 2 cosec (πx)	∞	2	∞	-∞	-2	-∞	∞	2

Thus, the required curve is