PLEAAAAAASE HELP!!!!!!! will give medal!

- anonymous

PLEAAAAAASE HELP!!!!!!! will give medal!

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- katieb

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- AkashdeepDeb

Use trigonometry here!
Tan x = 9000/6000

- anonymous

I tried that and still didn't get the right answer @AkashdeepDeb

- DebbieG

Do you know what to do with
\(\Large \tan(x)=\dfrac{9000}{6000}\) to find x?

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## More answers

- anonymous

I divide 9000/6000 right?

- DebbieG

That will reduce the fraction that tan(x)= but wont tell you x.

- anonymous

I don't understand? How do i solve it?

- DebbieG

Sorry, had a phone call.
You have \(\Large \tan(x)=\dfrac{9000}{6000}\) which reduces, so just for ease let's do that, and you get
\(\Large \tan(x)=\dfrac{3}{2}\)
right?

- DebbieG

Now, you are looking for the ANGLE, x, that solves \(\Large \tan(x)=\dfrac{3}{2}\), right?
That is, whatever (acute) angle makes that true, is the angle of depression that you are looking for, right?
Does that much make sense?

- anonymous

The first part makes sense but i still dont follow on the second part

- DebbieG

OK, tell me which part doesn't make sense. I kind of thought that was just one part... lol. Do you understand how @AkashdeepDeb set up the equation
\(\Large \tan(x)=\dfrac{9000}{6000}\)
from the problem description and diagram?
(I'm assuming so, since you said you already had that much.)

- DebbieG

And then, do you understand that I simply reduced that fraction to make it
\(\Large \tan(x)=\dfrac{3}{2}\)
which, strictly speaking, wasn't really necessary but is just easier to look at and type. :) And it's equivalent, anyway, so it doesn't hurt anything to do so.

- anonymous

okay yes i follow, i just dont understand how i get x

- DebbieG

OK, that's fine, we're going there next. :)

- DebbieG

So we have that \(\Large \tan(x)=\dfrac{3}{2}\). Think about what that MEANS.
It means that x (the angle we're looking for) is some angle that has, as the value of its tangent, the number 3/2.
That is, when the tangent function takes our unknown angle x as an "input", it gives us the number 3/2 as an "output".
Good so far?

- anonymous

yes

- DebbieG

Now what we want is to find our x. So what we NEED is something that turns that around.
We need something that lets us "input" a tangent VALUE, and takes it and gives us an "output" of the ANGLE MEASURE that HAS THAT as its tangent value.

- DebbieG

Do you know anything like that?
Maybe.... say..... another function? That flips the tangent function around like that?

- anonymous

no, the lesson that was supposed to teach me how to do this was only 3 pages long and very vague. So i don't know how to do this at all

- DebbieG

Are you sure it doesnt mention either the arctan function
\(\Large y=\arctan(x)\)
Or, it might refer to it as the "inverse tangent function"
\(\Large \tan^{-1}(x)\)
They are the same thing, just can be called by either name.

- anonymous

Deffinitley did not see anything about that... ive re-read the entire lesson atleast 6 times trying to firgure it out on my own, ive even tried the previous lesson, and the one after it

- DebbieG

But if not - that's ok - then all that matters is that inverse tangent function is the INVERSE of the TANGENT function.
As for any function and inverse, it "flips around" the inputs and outputs. so in
\(\Large y=\tan^{-1}(x)\)
Your INPUT x is a TANGENT VALUE. Then your OUTPUT y is an ANGLE MEASURE. You can do this in radians OR degrees, same meaning, and here you obviously want degrees.
There is also one other "technical" restriction on the inverse trig functions, and for tangent that is that it will always give you an angle between -90* and 90*. The reasons for that are not important here, and won't affect your answer since your angle is obviously between 0* and 90* (I just didn't want to be remiss in mentioning it). :)

- DebbieG

So, your calculator should have a button that looks like that function
\(\Large [\tan^{-1}(x)]\)
On a TI-83 it's a "2nd" function, just above the [TAN] button.
So to find the angle x such that
\(\Large \tan(x)=\dfrac{3}{2}\)
you simply need to evaluate
\(\Large \tan^{-1}(\dfrac{3}{2})\)
which is, by the definition of the inverse function, "the angle between 0* and 90* that has a tangent value of 3/2".

- DebbieG

(Make sure your calculator is in degree mode, so that it gives you the output in degrees. if you are in radian mode, it will give you x in RADIANS, not in DEGREES.)

- anonymous

@DebbieG I got 56.31! Is that right?

- DebbieG

Yessiree! :)

- DebbieG

But what I REALLY hope is that you have a bit of an understanding about the inverse function, now. :) It's very handy in trig! :)

- anonymous

omg thank you so much! That makes so much more sense. My calculator was in 1st degree mode when i was trying to solve

- DebbieG

You're welcome, happy to help. :)

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