# 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= , 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

## The function cosec x

What properties do you know about the function cosec (x)?

## The function sec x

What properties do you know about the function sec (x)?

## The function cot x

What properties do you know about the function cot (x)?