+1124 Good day all you good people!,
I have something here I need to understand..please help me:
If I had: \((5-3)\), and for no reason off course, I wanted to remove the "-", it would turn into this:
\(-(-5+3)\).
Now, in trigonometry I found this:
\(sin(-@-90) =sin(-(@+90)) \)
sorry, I use this "@" for Theta
The above makes sense, however another sum looks like this:
\(tan(@-180) =tan(-(@+180)\),
why is it not \(tan(-(-@+180)\)?
Thank you for your time with this, I do appreciate...
+118673 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
https://www.desmos.com/calculator/foqjyque7o
I hope that helps :)
+1124 Hi Melody,
just as I had suspected, The book is wrong for they indicate that;
tan(@-180) = tan(-(@+180))..
I thought that was incorrect. Thank you soo much for verifying for me....
just..how do you get the theta sign?.. 
+118673 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 :)
+1124 Thank you Melody, may I please just conclude:
This is WRONG:
\(tan(\theta-180)\)
\(=tan(-(\theta+180))\)
\(=-tan(\theta+180) \)
\(=-tan(180+\theta)\)
\(=-tan\theta\)
And this is RIGHT:
\(tan(\theta-180)\)
\(=tan(-(-\theta+180))\)
\(=-tan(-\theta+180) \)
\(=-tan(180-\theta)\)
\(=tan\theta\)
Thank you sooo much!!!
+118673 If you want to check you can put your functions into Desmos.
https://www.desmos.com/calculator
Just replace the theta with an x and put them equal to y.
If they are the same the graphs will overlap identically.
You wrote some excellent LaTex too!
There is a sticky note on latex (to the lower right of the screen)
And there is a heap of info on the web as well.
If you right click on anyone's latex you can chose to see the coding too.
Useful next suggestion:
To go to a new line just click \\ 
