Question

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

Answer 1

@dangerousjesse any luck?

Answer 2

@phi @vineeth10

Answer 3

@ganeshie8 @MATHMALE

Answer 4

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

Answer 5

@phi i just figured it out actually!! C right? and could you please help me with one more!! im stuck on it :/

Answer 6

Simplify \[\sqrt{\left( 1-\sin \Theta \right)\left( 1+\sin \Theta \right)}\]

Answer 7

@phi i have no idea what to do

Answer 8

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

Answer 9

For some reason i divided 16 in 2 idk why haha thank you!!

Answer 10

any idea what the answer is for your first question?

Answer 11

b right?

Answer 12

any idea on how to solve the second one? i really have no idea what to do @phi

Answer 13

do you know how to multiply the two binomials inside the square root
(some people use FOIL)

Answer 14

if you don't see
http://www.khanacademy.org/math/algebra/multiplying-factoring-expression/multiplying-binomials/v/multiplying-binomials

Answer 15

yeah when i foil i get sqrt(1-sin O)

Answer 16

is that right? @phi

Answer 17

can you show your work?

Answer 18

F: 1*1=1
O: 1*sinO=sinO
I: -sinO*1=-sinO
L: -sinO*sinO=-sin2
so its sqrt(1-sin^2) oops!

Answer 19

these are my options btw @phi
±sin Θ

|cos Θ|

±tan Θ

square root sine theta

Answer 20

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
\[ \cos^2 x= 1 - \sin^2 x \]

Answer 21

would it be B?

Answer 22

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 |

Answer 23

@phi thank you so so much!! i really truly appreciate it :)

Answer 24

yw