+118735 
+118735 Sun 15/3/15
1) What happened on this day in 1879? Thanks AlbertEinstein
2) Interesting probability - students in a circle Melody, Alan and CPhill
3) Manipulating logs Thanks anon
4) How many 3 digit numbers are multiples of 7 Thanks Alan
5) Estimating the sqrt(6) without using the sqrt key. Thanks CPhill and Melody.
6) Combinations. 3 mathematicians, 3 answers, nothing like variety. Thanks Alan, Melody and CPhill.
7) Permutations - How many words can be formed. Melody
8) Another circle permutations queston Melody
9) Poker (we all got it wrong) Thanks Alan, CPhill and Melody
Here is a useful website that CPhill found for us. http://en.wikipedia.org/wiki/Poker_probability
♫♪ ♪ ♫ ♬ ♬ MELODY ♬ ♬ ♫♪ ♪ ♫
+118735
How cot inverse (x) is (pie - tan inverse (1÷ x) ) and sec inverse x is simply cos inverse (1÷x) when x
Lets see if I can make sense of your question :)
How come $$cot^{-1}(x)\;\; is\;\;\; \pi - tan^{-1}\left(\frac{1}{x}\right)$$
and $$sec^{-1}(x)=cos^{-1}\left(\frac{1}{x}\right) \qquad when\;\; x <0 ?$$
from my graphs I can see that
cos and sec graphs https://www.desmos.com/calculator/3ekbqgy7ve
Cot and tan graph https://www.desmos.com/calculator/j1xb33odx7
$$\\sec^{-1}x=cos^{-1}\left(\frac{1}{x}\right)\qquad $when $ x\le-1\;\;and\;\; x\ge 1\\\\
cot^{-1}(x)= tan^{-1}\left(\frac{1}{x}\right)\qquad when\;\;x>0\\
and\\
cot^{-1}(x)=\pi\;\textcolor[rgb]{1,0,0}{+}\; tan^{-1}\left(\frac{1}{x}\right)\qquad when\;\;x<0\\\\$$
I have been mucking around with this and I need to give it more thought.
Perhaps another mathematician would like to jump in here.
