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:
Stacey Warren - Expert brainly.com
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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!!
any idea what the answer is for your first question?
any idea on how to solve the second one? i really have no idea what to do @phi
do you know how to multiply the two binomials inside the square root
(some people use FOIL)
if you don't see
yeah when i foil i get sqrt(1-sin O)
is that right? @phi
can you show your work?
so its sqrt(1-sin^2) oops!
these are my options btw @phi
square root sine theta
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
\[ \sin^2 x = 1 - \cos^2 x \]
\[ \cos^2 x= 1 - \sin^2 x \]
would it be B?
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 :)