I'm not sure of your background with modular arithmetic, so I'll just start small...
We consider all numbers with the same remainder after dividing by n to be EQUIVALENT.
For example, 2 = 5 = 8 = 11 = 300000000000002 = -1 mod 3. (Here, the "triple" bar sign would be better than the double bar...
sec(3t) = 2
invert (flip) both sides
cos(3t) = 1/2
Get a unit circle. Each point is of the form (cosine(angle), sine(angle))
We want the angles where cosine is 1/2.
These angles are:
π/3 and 5π/3
But since we have 3t, we include all solutions less than 6π. See the above reply for more details...
Have you ever seen P = e^{rt} before?
Usually, I would recommend exponential growth/decay for bacteria situations.
Furthermore,
"Doubling" and "halving" are very closely related!
Since this was the first hit when I Googled my homework, I'll resurrect this thread with my thoughts.
This holds trivially for prime numbers.
Claim: For n "square-free", \mathbb{Z}_n is (up to isomorphism) the unique abelian group of order n.
We extend the fact that \mathbb{Z}_{ab} \cong...
I guess so! There was another "seemingly active thread" about closed form expressions that caught my eye today, as did the fact that some first-poster had resurrected it after years of inactivity...
Cancel a factor of h from top and bottom. Then let h -> 0 and you'll get
\frac{-2}{x^2+2x+1} = \frac{-2}{(x + 1)^2}
Later, when you learn "shortcuts" (i.e rules of differentiation that will be proven), this second form will look a lot more familiar.
TsAmE, I might add that Calculus *methods* are not appropriate for this problem (even though it might appear in a calc book/course).
This is more about, as Mark44 has mentioned, coterminal angles and the domain of inverse trig functions.
Some people have an easier time working with degrees at...