# Math Help - trig function word problem #1

1. ## 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.

2. Originally Posted by skeske1234
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.