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 = 45°, what is the area of the opening?

Answer 1

4.8 in2

9.0 in2

19.3 in2

20.8 in2

Answer 2

@robtobey

Answer 3

@Preetha

Answer 4

@phi

Answer 5

@PeterPan

Answer 6

@dan815

Answer 7

@TheCatMan
@phi
@PeterPan
@campbell_st

Answer 8

They did not make you find the equation ... they told you it. Now use it.
A(Θ) = 16 sin Θ • (cos Θ + 1)

with Θ = 45°
(which is one of the angles where people memorize the sin , cos and tan of)
See http://www.allmathwords.org/en/e/exactvaltrig.html
for a short table. Use those values in your equation.

can you do that ?

Answer 9

k

Answer 10

i dont get it

Answer 11

although, based on the decimal answers, you can just use a calculator

Answer 12

what would i put in the calculator?

Answer 13

are you saying you can't read
A(Θ) = 16 sin Θ • (cos Θ + 1)
?

16 means 16
usually we do not bother to put in a multiplication sign,
and 16 sin Θ means 16 times sin Θ
in this case Θ is 45 degrees
so you do
16 times sin(45)
what do you get (from your calculator) ?

Answer 14

i dont know how to input the sin

Answer 15

or the cos

Answer 16

i have a a scientific calculator

Answer 17

why don't you take a few minutes and practice.
type sin 30
enter
what do you get for an answer?

Answer 18

or
sin 30 =

Answer 19

.5

Answer 20

ok, good. sin(30º)= ½ = 0.5

now do sin 45 =

Answer 21

.707

Answer 22

yes.

so you can do sin

now let's do the problem
A(Θ) = 16 sin Θ • (cos Θ + 1)

let's do the stuff inside the parens first
do cos 45 =

Answer 23

cos 45 is the same thing mate

Answer 24

yes, sin45 = cos45

now do
+ 1 =
it should add 1 to 0.707 to give 1.707

Answer 25

k i did it

Answer 26

if it says 1.707 you are good to continue
type in
x sin 45

Answer 27

my calculator is in degrees mode

Answer 28

thats how its supposed to be right?

Answer 29

yes, I know it is in degree mode (they gave us theta= 45º the circle means degrees)

Answer 30

i got 46

Answer 31

is that right?

Answer 32

we lost the bubble somewheres.

start over and be careful.
cos 45 + 1 =
what do you get ?

Answer 33

1.707

Answer 34

now type
x sin 45 x 16 =

Answer 35

there is no x key do you want me to multiply?

Answer 36

yes, whatever the multiply key is

Answer 37

oh

Answer 38

sorry im used to seeing a dot for multipliation

Answer 39

I was looking at my calculator and it has an "x"

Answer 40

19.31

Answer 41

im using the windows calculator app

Answer 42

so some symbols are different

Answer 43

yes.

if your calculator has parens you can type in
16 * sin 45 * ( cos 45 + 1) =
in one line.

Answer 44

is 19.31 the right answer?

Answer 45

yes, that looks good

Answer 46

thanks could you help with another?

Answer 47

ok

Answer 48

What sine function represents an amplitude of 1, a period of 2π, a horizontal shift of π, and a vertical shift of −4?

f(x) = sin (x − π) − 4

f(x) = sin (πx) + 4

f(x) = sin (x + pi over 2) + 4

f(x) = sin (pi over 2x) − 4

Answer 49

how would i start this off?

Answer 50

you use the "generic" equation
\[ A \sin\left( \frac{2 \pi}{T} x - B\right)+C \]

A is the amplitude
T is the period
B is the horizontal shift
C is the vertical shift

they told you A, T, B and C
put them in, simplify where possible, and what do you get ?

Answer 51

k let me solve

Answer 52

wait what do i do for the x

Answer 53

@phi

Answer 54

the x stays as is

Answer 55

k thanks man im sorry for bugging you

Answer 56

any progress?

Answer 57

f(x) = sin (x − π) − 4
is this the answer @phi

Answer 58

yes

Answer 59

k one more or no?

Answer 60

because your a great help man