You can hopefully see from the diagram above, that if we add to our
angle , we would come ‘full circle’ (ba-dum tish) and be back where we started from (think of it as adding 360 degrees if it makes you happier).
And since csc and sec are basically just utilisations of sin and cos, then they have the same property:
Now has a periodic cycle half the size of , which you can perhaps visualise easily by studying their respective plots side by side:
and so :