Graphs of Reciprocal Trigonometric Functions

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The discussion revolves around a homework problem involving the relationship between the height of a hill, the angle of inclination, and the length of a road built on that slope. It establishes that the length of the road can be expressed as d = h csc x, linking trigonometric functions to the geometry of the situation. Participants are encouraged to sketch diagrams and graphs to visualize the problem, particularly focusing on the behavior of the function as the angle approaches zero. There is a strong emphasis on understanding the concepts rather than just obtaining answers, highlighting the importance of grasping the underlying mathematics for future tests. The collaborative nature of the forum is appreciated for aiding in problem-solving.
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Homework Statement



A road is built up the slope of a hill with a height of h meters and an angle of inclination of x. The length of the road is d.

a) Sketch a diagram of this situation. Label all quantities.

b) Show that the length of the road is represented by the relation d = h csc x.

c) Determine the length of a road that ascends a hill of height 100m at an angle of 0.3. Round your answer to the nearest tenth of a meter.

d) Sketch a graph of d = h csc x for a hill of height 100m and on the interval x ε [0, pi/4].

e) Interpret the meaning of the graph as x approaches 0.I'm really lost here, if anyone can point me in the right direction, or give me an idea on how to go about solving it I'd really appreciate it. Please just don't give me the answer, I really want to try and figure this out so when it comes to test time I know! ;)

Thanks in advance! This forum is a blessing as well as all the members on it who contribute so willingly!
 
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What part of this don't you understand?
A road is built up the slope of a hill with a height of h meters and an angle of inclination of x. The length of the road is d.
There's probably a triangle lurking in this description.
 

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