The length s of a shadow cast by a vertical gnomon(a device used to tell time)of height h when theangle of the sunabove the horizonis θ can be modeledby the equations = h sin(90° − θ)sin θ ,0° < θ ≤ 90°.(a) Verify that the expression for s is equal to h cot θ.(b) Use a graphing utility to create a table of thelengths s for different values of θ. Let h = 5 feet.(c) Use your table from part (b) to determine theangle of the sun that results in the minimumlength of the shadow.(d) Based on your results from part (c), what time ofday do you think it is when the angle of the sunabove the horizon is 90°? cos x - csc x cot x. Show that the expression for therate of change can also be written as - cos x cot? x.62. Shadow Length • • ·• The length s of a shadow cast by a vertical gnomon: (a device used to tell time)of height h when the• angle of the sun: above the horizonis e can be modeled: by the equationh sin(90° – 0)sin 0: ° < 0 < 90°.: (a) Verify that the expression for s is equal to h cot 0.(b) Use a graphing utility to create a table of thelengths s for different values of 0. Let h = 5 feet.: (c) Use your table from part (b) to determine theangle of the sun that results in the minimumlength of the shadow.(d) Based on your results from part (c), what time ofday do you think it is when the angle of the sunabove the horizon is 90°?ExplorationMORANS

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Trigonometry (MindTap Course List)

8th Edition

ISBN:9781305652224

Author:Charles P. McKeague, Mark D. Turner

Publisher:Charles P. McKeague, Mark D. Turner

Chapter4: Graphing And Inverse Functions

Section: Chapter Questions

Problem 2GP

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The length s of a shadow cast by a vertical gnomon
(a device used to tell time)
of height h when the
angle of the sun
above the horizon
is θ can be modeled
by the equation
s = h sin(90° − θ)
sin θ ,
0° < θ ≤ 90°.
(a) Verify that the expression for s is equal to h cot θ.
(b) Use a graphing utility to create a table of the
lengths s for different values of θ. Let h = 5 feet.
(c) Use your table from part (b) to determine the
angle of the sun that results in the minimum
length of the shadow.
(d) Based on your results from part (c), what time of
day do you think it is when the angle of the sun
above the horizon is 90°?

cos x - csc x cot x. Show that the expression for the
rate of change can also be written as - cos x cot? x.
62. Shadow Length • • ·
• The length s of a shadow cast by a vertical gnomon
: (a device used to tell time)
of height h when the
• angle of the sun
: above the horizon
is e can be modeled
: by the equation
h sin(90° – 0)
sin 0
: ° < 0 < 90°.
: (a) Verify that the expression for s is equal to h cot 0.
(b) Use a graphing utility to create a table of the
lengths s for different values of 0. Let h = 5 feet.
: (c) Use your table from part (b) to determine the
angle of the sun that results in the minimum
length of the shadow.
(d) Based on your results from part (c), what time of
day do you think it is when the angle of the sun
above the horizon is 90°?
Exploration
MORANS

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