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Good day all you good people!,

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Good day all you good people!,

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

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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
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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.

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