(a) Let x represent the number of feet from the screen to a seat. Using trigonometry, explain why 0 is given by (2). 0 = arctan - arctan (b) Notice that if we change x, then the angle 0 will also change. This means 0 (x) = arctan - arctan

Trigonometry (MindTap Course List)
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Author:Charles P. McKeague, Mark D. Turner
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Chapter1: The Six Trigonometric Functions
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Parts A and B are a part of the same question

2. (MG 19 S11 Purple 2) You really miss going to the movies and would like to create your own makeshift theater.
You go online and find a cheap projector and a screen that is 6 feet tall. Once you have everything set up, you
want to figure out where to sit and get the best view. Naturally, you pull out a pen and pencil and think about
trigonometry! First you observe that from any seat, your eye level is 3 feet from the bottom of the screen. You
also notice that in order to get the best view, you want the angle formed by your line of sight between the top and
bottom of the screen to be as large as possible.
6 ft
screen
3 ft
x ft
from the screen
(a) Let x represent the number of feet from the screen to a seat. Using trigonometry, explain why 0 is given by
(?)
(2)
0 = arctan
- arctan
(b) Notice that if we change x, then the angle 0 will also change. This means
0 (x)
(2)
= arctan
- arctan
is a function with input x and output 0. Use DESMOS to graph 0(x) and find which x will give you the
largest value of 0. This is then how far from the screen you have to sit to get the best view!
Transcribed Image Text:2. (MG 19 S11 Purple 2) You really miss going to the movies and would like to create your own makeshift theater. You go online and find a cheap projector and a screen that is 6 feet tall. Once you have everything set up, you want to figure out where to sit and get the best view. Naturally, you pull out a pen and pencil and think about trigonometry! First you observe that from any seat, your eye level is 3 feet from the bottom of the screen. You also notice that in order to get the best view, you want the angle formed by your line of sight between the top and bottom of the screen to be as large as possible. 6 ft screen 3 ft x ft from the screen (a) Let x represent the number of feet from the screen to a seat. Using trigonometry, explain why 0 is given by (?) (2) 0 = arctan - arctan (b) Notice that if we change x, then the angle 0 will also change. This means 0 (x) (2) = arctan - arctan is a function with input x and output 0. Use DESMOS to graph 0(x) and find which x will give you the largest value of 0. This is then how far from the screen you have to sit to get the best view!
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