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# Good day all you good people!,

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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...

Nov 1, 2018
edited by juriemagic  Nov 1, 2018
edited by juriemagic  Nov 1, 2018
edited by juriemagic  Nov 1, 2018

#1
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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 :)

Nov 1, 2018
edited by Melody  Nov 1, 2018
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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?.. juriemagic  Nov 1, 2018
edited by juriemagic  Nov 1, 2018
#3
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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 :)

Melody  Nov 1, 2018
edited by Melody  Nov 1, 2018
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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!!!

juriemagic  Nov 1, 2018
edited by juriemagic  Nov 1, 2018
edited by juriemagic  Nov 1, 2018
edited by juriemagic  Nov 1, 2018
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YES that appears to be correct. Melody  Nov 1, 2018
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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    \\ Melody  Nov 1, 2018
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you've been very kind...thank you,...have a blessed day!!

juriemagic  Nov 1, 2018
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You are very welcome.

I am always keen to share my knowledge, and my enthusiasm for mathematics, with those that really want to learn.

In fact I thrive on the opportunity!

The other regular answerers feel this way too. Melody  Nov 1, 2018
edited by Melody  Nov 1, 2018