# Trigonometric function of x

The angle of elevation from the top of a house to a jet flying 2 miles above the house is x radians. If d represents the horizontal distance, in miles, of the jet from the house, express d in terms of a trigonometric function of x. The graph the function for 0< x <pi.

Dick
Homework Helper
Did you draw a right triangle involving x, d and 2 miles? That's a good place to start.

yes I did, now what?

LCKurtz
Homework Helper
Gold Member
From your triangle with d, x, and 2 labeled can you think of a trig function that involves them?

no, thats why I am asking...

ok, this is what I need to figure out. tan x=opp/adj = ?/?

Dick
Homework Helper
ok, this is what I need to figure out. tan x=opp/adj = ?/?

Very much so. Skip the last = ?/?. Just substitute the values for opp and adj.

well if I knew what they were I could..lol

maybe this graph will help..

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Dick
Homework Helper
well if I knew what they were I could..lol

I'm starting to feel helpless here. You drew the picture, right? It should be right in front of you. Which is the adjacent side and which is the opposite side to the angle x?

Dick
Homework Helper
maybe this graph will help..

How can you not know with such a gorgeous picture to help? Which leg is opposite the angle x and which is adjacent?

the 2 mile side would be the opposite and the other would be the adjacent side.

I have never done this before, so that is why I am lost...No I didnt draw the picture. It is supposed to help me.

Dick
Homework Helper
the 2 mile side would be the opposite and the other would be the adjacent side.

Yes, so tan(x)=... just fill it in.

tan(x)=2/? Grrrrrr

Dick
Homework Helper
the 2 mile side would be the opposite and the other would be the adjacent side.

No offense, but this is getting to be like pulling teeth. The 'other' i.e. the 'adjacent side' is clearly labelled in your picture. It has a letter on it.

tax(x)=2/d

I do understand your frustration with me, just think how I feel.. :(

I was wondering why do I need to forget the ?/?....

Dick
Homework Helper
I was wondering why do I need to forget the ?/?....

I just meant you should fill in the ??'s. tan(x)=2/d is exactly what you want. You are basically done. Now just solve for d.

I truly don't know how to solve for d. I must sound pretty stupid, huh?

ok wait, is it d=2cot(x) ?

oops, I mean 2/tan(x)

Dick
Homework Helper
ok wait, is it d=2cot(x) ?

Sure. That's more than brilliant. I was hoping for just d=2/tan(x). But that's the same if not better.

Dick