MHB Trigonometric functions: Sec, Cot, Csc

[Petrus]

Hello,
Im currently on chapter about derivate trigonometric functions. It have been hard for me to understand this sec,cot,-csc? Why do you rewrite example $1/cos^2x$ as $sec^2x$? when I get like sec,csc etc i kinda feel i have no clue what it means. Then you think what do Petrus mean? example I know cos 0 =1 and then will $sec^2(0)=1$ but there is many more and I wounder how much should I know about this sec,cot,-csc? If I am honest i keep forgeting $sec^2x=1/cos^2x$ Is there any trick to memorise these:)
Thanks.

 

[Ackbach]

I always write these other trig functions in terms of $\sin$ and $\cos$, and then use the quotient rule to differentiate. You might find http://www.mathhelpboards.com/f12/trigonometry-memorize-trigonometry-derive-35/ helpful in narrowing down what you should have memorized.