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 [br][math]cosec\left(x\right)=\frac{1}{sin\left(x\right)},[/math][math]sec\left(x\right)=\frac{1}{cos\left(x\right)},[/math][math]cot\left(x\right)=\frac{1}{tan\left(x\right)}[/math][br]To sketch these graphs we need to find the values of the functions when x = 0, x=[math]\frac{\pi}{2}[/math], x= [math]\pi[/math], x= [br][math]\frac{3\pi}{2}[/math], x=[math]2\pi[/math][br]Then we need to find any asymptotes.[br]The functions have been sketched using GeoGebra below for you.

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