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Math Help - trig function word problem #1

  1. #1
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    trig function word problem #1

    When the sun is at an angle of elevation x, a tree with height 12 m casts a shadow of length, s, in metres.

    a) show that the length of the shadow can be modelled by the relation s=12cotx

    b) sketch a graph of s=12cotx on the interval XE[0, 2pi]

    c) interpret the meaning of the graph as x approaches 0 and as x approached pi/2

    I don't understand this question. I know that a graph y=tanx has a branch that goes through the orgin, and that cotx's graph is the reflection in the y-axis and shifted pi/2 right of y=tanx's graph. So, why is cotx right in this question and not tanx? I don't know how to do any of these three questions. Please help, Thanks.
    Last edited by mr fantastic; August 12th 2009 at 04:20 PM. Reason: Changed post title
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  2. #2
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    Quote Originally Posted by skeske1234 View Post
    When the sun is at an angle of elevation x, a tree with height 12 m casts a shadow of length, s, in metres.

    a) show that the length of the shadow can be modelled by the relation s=12cotx

    b) sketch a graph of s=12cotx on the interval XE[0, 2pi]

    c) interpret the meaning of the graph as x approaches 0 and as x approached pi/2

    I don't understand this question. I know that a graph y=tanx has a branch that goes through the orgin, and that cotx's graph is the reflection in the y-axis and shifted pi/2 right of y=tanx's graph. So, why is cotx right in this question and not tanx? I don't know how to do any of these three questions. Please help, Thanks.
    1. Draw a sketch.

    2. You are dealing with a right triangle. Let h denote the height of the tree and s the length of the shadow then you get:

    \tan(x)=\dfrac hs~\implies~\cot(x)=\dfrac sh ~\implies~\boxed{s=h \cdot \cot(x)}

    to c): When x = 0 (at sunrise) the rays of sunlight are parallel to the surface of the earth and then the shadow will be infinitely long.
    When x = \pi (at sunset) the rays of sunlight are parallel to the surface of the earth and then the shadow will be infinitely long.
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