Trigonometry Derivatives
While you may know how to take the derivative of a polynomial, what happens when you need to take the derivative of a trig function? What IS the derivative of a sine?
Luckily, the derivatives of trig functions are simple -- they're other trig functions! For example, the derivative of sine is just cosine:
The rest of the trig functions are also straightforward once you learn them, but they aren't QUITE as easy as the first two.
Derivatives of Trigonometry Functions
sin'(x) = cos(x)
cos'(x) = -sin(x)
tan'(x) = sec2(x)
sec'(x) = sec(x)tan(x)
cot'(x) = -csc2(x)
csc'(x) = -csc(x)cot(x)
Take a look at this graphic for an illustration of what this means. At the first point (around x=2*pi), the cosine isn't changing. You can see that the sine is 0, and since negative sine is the rate of change of cosine, cosine would be changing at a rate of -0.
At the second point I've illustrated (x=3*pi), you can see that the sine is decreasing rapidly. This makes sense because the cosine is negative. Since cosine is the rate of change of sine, a negative cosine means the sine is decreasing.
