Right now, I'm taking a little break from studying Calculus today. Before leaving for Ilocos, I studied the derivative of logarithms (a.k.a. logarithmic differentiation... Okay I sound so smart but really I'm struggling with all the things one must remember...) and while everything is a bit hazy, I didn't review much when I got back and immediately continued on, finding myself face to face with trigonometry once again.
Now trigonometry is one of my favorite math topics despite my slow speed in solving and/ or proving because I'm so used to drawing circles and determining formulas all on my own every time I solve a trigonometric function. Sometimes I get frustrated because I can't seem to just memorize the formulas, but in the end, I pride myself at being able to derive formulas from the ones I already know by heart.
So just to share, here are the the derivatives of trigonometric functions as well as the derivatives of the inverse of trigo functions. (Just hoping that everytime I see them here in my blog they'll get stuck to my brain LOL):
1. d/dx sin x= cos x
2. d/dx cos x= -sin x
3. d/dx tan x= sec^2 x
4. d/dx cot x= -csc^2 x
5. d/dx sec x= sec x tan x
6. d/dx csc x= -csc x cot x
1. d/dx arcsin x= 1/ (sqrt (1-x^2))
2. d/dx arccos x= -1/ (sqrt (1-x^2))
3. d/dx arctan x= 1/ (1+x^2)
4. d/dx arccot x= -1/ (1+x^2)
5. d/dx arcsec x= 1/ ( |x| sqrt (x^2-1))
6. d/dx arccsc x= -1/ ( |x| sqrt (x^2-1))
Actually the derivatives of the inverse are a bit easier to remember because they come in pairs. Derivatives of arcsin and arccos are almost same except one is positive and the other is negative. The same goes for the pairs arctan/arccot and arcsec/arccsc.
It's been a while since I last did trigo, which was in the summer of 2010 when I enrolled in Math 17 (Algebra and Trigonometry) just to see how difficult it really is. I got two perfect scores out of five quizzes but unfortunately I flunked the final exam because I was overwhelmed by the number of items and we just had one hour to finish. (Deriving formulas ate up most of my time, you see.)
Now I'm hoping to somehow be able to use this knowledge for mapping sites. It would be very cool to be able to create a map of an irregularly shaped site.
And I also need to relearn how to use the scientific calculator if I want to get answers fast.
Now trigonometry is one of my favorite math topics despite my slow speed in solving and/ or proving because I'm so used to drawing circles and determining formulas all on my own every time I solve a trigonometric function. Sometimes I get frustrated because I can't seem to just memorize the formulas, but in the end, I pride myself at being able to derive formulas from the ones I already know by heart.
So just to share, here are the the derivatives of trigonometric functions as well as the derivatives of the inverse of trigo functions. (Just hoping that everytime I see them here in my blog they'll get stuck to my brain LOL):
1. d/dx sin x= cos x
2. d/dx cos x= -sin x
3. d/dx tan x= sec^2 x
4. d/dx cot x= -csc^2 x
5. d/dx sec x= sec x tan x
6. d/dx csc x= -csc x cot x
1. d/dx arcsin x= 1/ (sqrt (1-x^2))
2. d/dx arccos x= -1/ (sqrt (1-x^2))
3. d/dx arctan x= 1/ (1+x^2)
4. d/dx arccot x= -1/ (1+x^2)
5. d/dx arcsec x= 1/ ( |x| sqrt (x^2-1))
6. d/dx arccsc x= -1/ ( |x| sqrt (x^2-1))
Actually the derivatives of the inverse are a bit easier to remember because they come in pairs. Derivatives of arcsin and arccos are almost same except one is positive and the other is negative. The same goes for the pairs arctan/arccot and arcsec/arccsc.
It's been a while since I last did trigo, which was in the summer of 2010 when I enrolled in Math 17 (Algebra and Trigonometry) just to see how difficult it really is. I got two perfect scores out of five quizzes but unfortunately I flunked the final exam because I was overwhelmed by the number of items and we just had one hour to finish. (Deriving formulas ate up most of my time, you see.)
Now I'm hoping to somehow be able to use this knowledge for mapping sites. It would be very cool to be able to create a map of an irregularly shaped site.
And I also need to relearn how to use the scientific calculator if I want to get answers fast.
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