MHB Trigonometric functions: Sec, Cot, Csc

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Understanding secant (sec), cotangent (cot), and cosecant (csc) functions can be challenging, particularly in relation to their derivatives. The secant function is defined as the reciprocal of cosine, which is why $1/cos^2x$ is rewritten as $sec^2x$. It's important to memorize key identities like $sec^2x=1/cos^2x$ to aid in differentiation. Using sine and cosine to express these functions can simplify the process, and applying the quotient rule is a recommended strategy for differentiation. Familiarity with these functions and their derivatives is essential for mastering trigonometric calculus.
Petrus
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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.
 
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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.
 
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