Melody

I write my my maths in LaTex.

See the box in the ribbon above.  [I mean when you are creating a post]

Click into that and a box comes up in which you can input your latex coding.

You can start with very simple things and learn from there. Lots of people here will be happy to help you.

Latex is code that allows you to write mathematics things on the internet (it is a lot more than that really but that is what we use it for.)

anyway, open the LaTex input box and type in

tan(\theta-180)    then press "ok"

and this is what you weill get 

\(tan\theta\)

theta by itself is just coded as \theta 

Give it a go, LaTex coding is fun :)

Hi Juriemagic,

Not both are true but i expect that is because you made a typo.

Think about the cyclic nature of the tan function. It repeats every 180 degrees

If you consider it works on the unit circle, that should help.

\(tan\theta = tan(\theta\pm180k) \qquad \text{where k is an integer}\\ so\\ tan\theta = tan (\theta -180)=tan(-(-\theta+180))\\ also\\ tan\theta = tan(\theta+180)=tan(-(-\theta-180))\\ \\~\\ HOWEVER\\ tan \theta =tan(\theta-180)\ne tan(-(\theta+180))\\ but\\ tan \theta = -tan(-(\theta+180))\\\)

Here are some of those graphs

You have picked up a 

BR, or RR or RR card

You can see one red side the other side could be

B,R,R,R,R

So I think the probability that the other side is red is     4/5

Thanks Chris :)

I can do it too LOL

Yours is a little more impressive than mine though since you did not do it my way.

At least I do not think that you did. 

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sghgfhgrty

q2wer345

Thanks guest, my method is the same as yours but i have been asked to recreate in the way i have done in the past.

\(164x+37y=1\)

The method that guest and I both use was devised by the ancient Greek mathematician Euclid.

\(\text{Euclidean algorithm}\\ 164=4*(37)+16\\ 37=2*(16)+5\\ 16=3*(5)+1\\~\\ \text{Extended Euclidean algorith}\\ 1=16-3*(5)\\ 1=16-3*(37-2*(16))\\ 1=16-3*37+6*(16)\\ 1=-3*37+7*(16)\\ 1=-3*37+7*(164-4*(37))\\ 1=-3*37+7*164-28*(37)\\ 1=7*164-31*(37)\\~\\ 1=164(7)+37(-31)\\\)

So    x=7  and  y=-31 is one integer solution.

The question is now answered but I will continue in order to find all the possible solutions

\(1=164(7)+37(-31)\\ 1=164(7+37n)+37(-31-164n)\\ \text{I have added and then subtracted 164*37n}\\~\\ x=7+37n\qquad and \qquad y=-31-164n \qquad For\;\; all \;\;n\in Z\)

I am very glad I could help :)

On behalf of all our answerers I thank you.

We all try our hardest to help everyone and we always appreciated it when people say thanks and/or interact with us.

I would be interested in this answer too.