PLEASE HELP!! A rain gutter is to be constructed of aluminum sheets 12 inches wide. After marking off a length of 4 inches from each edge, this length is bent up at an angle Θ. The area A of the opening may be expressed as the function: A(Θ) = 16 sin Θ • (cos Θ + 1). If Θ = 90°, what is the area of the opening? When i plug 90 in i keep getting 15, but my choices are: 21.8 in2 16.0 in2 7.9 in2 1.0 in2

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PLEASE HELP!! A rain gutter is to be constructed of aluminum sheets 12 inches wide. After marking off a length of 4 inches from each edge, this length is bent up at an angle Θ. The area A of the opening may be expressed as the function: A(Θ) = 16 sin Θ • (cos Θ + 1). If Θ = 90°, what is the area of the opening? When i plug 90 in i keep getting 15, but my choices are: 21.8 in2 16.0 in2 7.9 in2 1.0 in2

Trigonometry
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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@dangerousjesse any luck?

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Other answers:

  • phi
first, you can do this without a calculator. But if you do use a calculator, be sure it is in degree mode. you should(!) know sin(90º)= 1 and cos(90º)= 0
@phi i just figured it out actually!! C right? and could you please help me with one more!! im stuck on it :/
Simplify \[\sqrt{\left( 1-\sin \Theta \right)\left( 1+\sin \Theta \right)}\]
@phi i have no idea what to do
  • phi
First, How did you get C 7.9? It seems if sin(90) is 1 and cos(90) is 0 you would do 16 sin Θ • (cos Θ + 1) 16 • 1 •(0+1) and now we add 0+1 (not *too* hard) and multiply that by 16*1 you don't get 7.9
For some reason i divided 16 in 2 idk why haha thank you!!
  • phi
any idea what the answer is for your first question?
b right?
any idea on how to solve the second one? i really have no idea what to do @phi
  • phi
do you know how to multiply the two binomials inside the square root (some people use FOIL)
  • phi
if you don't see http://www.khanacademy.org/math/algebra/multiplying-factoring-expression/multiplying-binomials/v/multiplying-binomials
yeah when i foil i get sqrt(1-sin O)
is that right? @phi
  • phi
can you show your work?
F: 1*1=1 O: 1*sinO=sinO I: -sinO*1=-sinO L: -sinO*sinO=-sin2 so its sqrt(1-sin^2) oops!
these are my options btw @phi ±sin Θ |cos Θ| ±tan Θ square root sine theta
  • phi
ok looks better there is a *very useful* identity you should remember for trig problems \[ \sin^2 x + \cos^2 x = 1 \] which you can rewrite as \[ \sin^2 x = 1 - \cos^2 x \] or \[ \cos^2 x= 1 - \sin^2 x \]
would it be B?
  • phi
yes. replace 1 -sin^2 with cos^2 inside the square root sqrt(cos^2) = cos is the only choice that looks close (they must only want the positive root) | cos Θ |
@phi thank you so so much!! i really truly appreciate it :)
  • phi
yw

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