The functions cosec x, sec x and cot x

The functions of cosec x, sec x, and cot x

In exercise 5.7 we briefly looked at how we can sketch the graphs of the reciprocal trigonometric functions. We can do this by finding the reciprocals of sin x, cos x and tan x at important points on the graphs. Where

To sketch these graphs we need to find the values of the functions when x = 0, x=

, x=

Then we need to find any asymptotes. The functions have been sketched using GeoGebra below for you.

The graphs of the functions cosec (x), sec (x) and cot (x)

For the following questions, think about the following properties: domain, range, period, symmetry, intervals of increase and decrease, vertical asymptotes, y-intercepts and x-intercepts