Trigonometric functions: Sec, Cot, Csc

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SUMMARY

This discussion focuses on the understanding and differentiation of trigonometric functions, specifically secant (sec), cotangent (cot), and cosecant (csc). The user expresses difficulty in grasping the meaning and application of these functions, particularly the identity $sec^2(x) = 1/cos^2(x)$. A suggestion is made to utilize the quotient rule for differentiation and to memorize relationships between these functions and sine and cosine. A resource link is provided for further assistance in memorization techniques.

PREREQUISITES
  • Understanding of basic trigonometric functions: sine, cosine, secant, cosecant, and cotangent.
  • Familiarity with differentiation rules, particularly the quotient rule.
  • Knowledge of trigonometric identities and their relationships.
  • Basic algebra skills for manipulating trigonometric expressions.
NEXT STEPS
  • Study the derivation of trigonometric identities, focusing on secant, cosecant, and cotangent.
  • Learn how to apply the quotient rule in differentiation of trigonometric functions.
  • Explore mnemonic techniques for memorizing trigonometric identities and functions.
  • Review the implications of $sec^2(x) = 1/cos^2(x)$ in calculus applications.
USEFUL FOR

Students studying calculus, particularly those focusing on trigonometric functions and their derivatives, as well as educators seeking effective teaching methods for these concepts.

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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