What does it mean written out?

Question

What exactly does mod stand for in calculus?
What about cosine, etc.

I mean actually written out if you had to use them by hand.

Answer 1

Mod is what you you get when you do an integer division that doesn't give you an integer as an answer. For example:

15/7 = 2 and 1/7

The number "15 mod 7" is 1 and describes the numerator in the fraction you see above. Observe that the denominator in the fraction has to be the same as the last argument in the mod statement.

Here are some other mod numbers:

15 mod 5 = 0 (15 / 5 = 3 and 0/15)
15 mod 6 = 3 (15 / 6 = 2 and 3/6)
0 mod 6 = 0
4000000 mod 5 = 0
1 mod 6 = 1
2 mod 6 = 2
3 mod 6 = 3
4 mod 6 = 4
5 mod 6 = 5
6 mod 6 = 0
7 mod 6 = 1

Hope this helps.

Answer 2

Mod is short for modulus. Written with two vertical lines enclosing the variable x, it simply means the numercial value of that variable ignoring the sign if any. Thus mod x and mod -x will be equal and will be equal to the numerical value of x.

sine, cosine, tangent, cotangent are trigonometrical properties of an angle when it forms part of a right angled triangle. Thus sine alpha or sine theta or sin x = height / hypotenuse, cosine x or cos x = base / hypotenuse, tan x = height / base and cotangent = base / height etc.

Answer 3

Does your calculator have (abs) on it?

Mod may also be used for modular arithmetic to find the remainder when one number is divided by another.

Thus 20 mod 6 = 2 because when 20 is divided by 6 the remainder is 2 (20 = 6*3 + 2)