Question

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?

21.8 in^2

16.0 in^2

7.9 in^2

1.0 in^2

Answer 1

@SithsAndGiggles

Answer 2

Plug in \(\theta=90^\circ\).
\[A(90^\circ)=16\sin90^\circ(\cos90^\circ+1)\]
What's the sine and cosine of 90 degrees?

Answer 3

pi/2?

Answer 4

and 3pi/2 (for 60 degree)

Answer 5

Where are you getting the 60 degrees from?

Recall the unit circle:

Answer 6

Oh, I did degree to radians

Answer 7

There's no need to convert to radians, unless you weren't sure that 90 degrees is \(\dfrac{\pi}{2}\) radians.

Do you understand that \(\cos90^\circ=0\) and \(\sin90^\circ=1\)?

Answer 8

i did that but i thought it was wrong

Answer 9

What do you with that?

Answer 10

\[A(90^\circ)=16\sin90^\circ(\cos90^\circ+1)=16\times1\times(0+1)=16\]

Answer 11

So, B?

Answer 12

yep

Answer 13

Oh, ok. Yaaay!!! Are you a trig- major or something?

Answer 14

Thanks

Answer 15

THANKYOU SOOO MUCHH THIS WAS CORRECT (JUST TOOK IT ON FLVS)