A community for students.
Here's the question you clicked on:
 0 viewing
LeventAChaves
 2 years ago
How can i remember all trig functions and their identities? I mean, its easy to remember what sin, cos, tan are but with cosecant, secant, cotangent, arccosine, arcsine, arctan i cant remember their derivatives and identities. Can you please give some advice? Thank you very much.
LeventAChaves
 2 years ago
How can i remember all trig functions and their identities? I mean, its easy to remember what sin, cos, tan are but with cosecant, secant, cotangent, arccosine, arcsine, arctan i cant remember their derivatives and identities. Can you please give some advice? Thank you very much.

This Question is Open

Topi
 2 years ago
Best ResponseYou've already chosen the best response.1I don't bother to remember others that sin, cos and tan including their inverses. IMHO secant and cosecant are totally useless and cotangent is only needed when tangent approaches infinity. What comes to the derivatives one only must remember that cosine starts as decreasing. So:\[\frac{ d }{ dx }\sin x = \cos x, \frac{ d }{ dx }\cos x = \sin x\]One can either remember tangent's derivative one or the other way:\[\frac{ d }{ dx }\tan x = 1+\tan^2x=\frac{ 1 }{ \cos^2x }\]But these can be derived from each other:\[\frac{ 1 }{ \cos^2x }=\frac{ (\cos^2x+\sin^2x) }{ \cos^2x }=1+\frac{ \sin^2x }{ \cos^2x }=1+\tan^2x\]The derivatives of the arccusfunctions can be calculated by the identity:\[\frac{ dy }{ dx }=\frac{ 1 }{ \frac{ dx }{ dy } }\]So we can easily see from the equation\[\frac{ d }{ dx }\tan x = 1+\tan^2x\] that\[\frac{ d }{ dx }\arctan x = \frac{ 1 }{1+x^2 }\]and because\[\sin^2x+\cos^2x=1\]that\[\frac{ d }{ dx }\arcsin x=\frac{ 1 }{ \sqrt{1x^2} }, \frac{ d }{ dx }\arccos x=\frac{ 1 }{ \sqrt{1x^2} }\]Hope that helped.

alffer1
 2 years ago
Best ResponseYou've already chosen the best response.0It's just a question of practice. Remember that sin^2 x + cos^2 x = 1, then you can easily derive that sec^2 = 1+tan^2 and csc^2 = 1+ cot^2x. That's for the Pythagorean identities. Topi wrote a great explanation of the derivatives.
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.