How to Graph the Horizontal Distance of a Jet from a House Using Trigonometry?

In summary: For example, when x=0, what is d?In summary, the angle of elevation from the top of a house to a jet flying 2 miles above the house is represented by x radians. The horizontal distance, d, of the jet from the house can be expressed as d=2/tan(x). By plotting points on a graph, the function can be visualized for 0<x<pi.
  • #1
lilchicadees
17
0
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.
 
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  • #2
Did you draw a right triangle involving x, d and 2 miles? That's a good place to start.
 
  • #3
yes I did, now what?
 
  • #4
From your triangle with d, x, and 2 labeled can you think of a trig function that involves them?
 
  • #5
no, that's why I am asking...
 
  • #6
ok, this is what I need to figure out. tan x=opp/adj = ?/?
 
  • #7
lilchicadees said:
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.
 
  • #8
well if I knew what they were I could..lol
 
  • #9
maybe this graph will help..
 

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  • #10
lilchicadees said:
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?
 
  • #11
lilchicadees said:
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?
 
  • #12
the 2 mile side would be the opposite and the other would be the adjacent side.
 
  • #13
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.
 
  • #14
lilchicadees said:
the 2 mile side would be the opposite and the other would be the adjacent side.

Yes, so tan(x)=... just fill it in.
 
  • #15
tan(x)=2/? Grrrrrr
 
  • #16
lilchicadees said:
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.
 
  • #17
tax(x)=2/d
 
  • #18
I do understand your frustration with me, just think how I feel.. :(
 
  • #19
I was wondering why do I need to forget the ?/?...
 
  • #20
lilchicadees said:
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.
 
  • #21
I truly don't know how to solve for d. I must sound pretty stupid, huh?
 
  • #22
ok wait, is it d=2cot(x) ?
 
  • #23
oops, I mean 2/tan(x)
 
  • #24
lilchicadees said:
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.
 
  • #25
lilchicadees said:
oops, I mean 2/tan(x)

2/tan(x)=2*cot(x).
 
  • #26
ok, now I need to use this information to fill out that graph. How would I go about that?
 
  • #27
lilchicadees said:
ok, now I need to use this information to fill out that graph. How would I go about that?

You could start by plotting some points.
 

FAQ: How to Graph the Horizontal Distance of a Jet from a House Using Trigonometry?

What is a "Trigonometric function of x"?

A trigonometric function of x is a mathematical function that relates the angles of a right triangle to the lengths of its sides. It is commonly used in the fields of mathematics, physics, and engineering.

What are the six main trigonometric functions?

The six main trigonometric functions are sine, cosine, tangent, cotangent, secant, and cosecant. They are abbreviated as sin, cos, tan, cot, sec, and csc respectively. Each function represents a ratio of two sides of a right triangle.

How are trigonometric functions used in real life?

Trigonometric functions are used in a variety of real-life situations, including navigation, surveying, and engineering. They are also used in physics to describe the motion of waves and in astronomy to calculate the positions of celestial objects.

What is the unit circle and how is it related to trigonometric functions?

The unit circle is a circle with a radius of 1 centered at the origin of a Cartesian coordinate system. It is used to define and visualize trigonometric functions. The coordinates of a point on the unit circle correspond to the sine and cosine values of a particular angle.

What is the relationship between trigonometric functions and right triangles?

The values of trigonometric functions are based on the ratios of the sides of a right triangle. The sine function is the ratio of the opposite side to the hypotenuse, the cosine function is the ratio of the adjacent side to the hypotenuse, and the tangent function is the ratio of the opposite side to the adjacent side. This relationship is known as the "SOH-CAH-TOA" rule.

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