Question

ANYBODY HELP !!!!!!

Answer 1

Which problem do you need help solving?

Answer 2

any

Answer 3

Okay, let's do the first one.
a. Find the length of side b to two decimal places.
b. Find the length of side a to two decimal places in three different ways.

Any idea how to tackle this?

Answer 4

yeah im sorry i knew that one. Can you help with the second one?

Answer 5

Okay, fine. Can you find the circumference of that circle? The angle can be found by this proportion:
\[\frac{15}{C} = \frac{\theta}{360}\] if \(C\) is the circumference.

Answer 6

5400/Ctheta?

Answer 7

i have till ten to get points!AHHHH

Answer 8

C = 12 pi
Replace C with 12 pi.
Multiply 15x360 and then divide by 12 pi. That will be the angle theta

Answer 9

theta = 450

Answer 10

Isn't all the way around the circle only 360 degrees? :-)

Answer 11

Seems too big since the entire circle would only be 360 degrees.

Answer 12

You forgot to divide by pi = 3.14...

Answer 13

oops sorry forgot the pi sign ooops

Answer 14

always look at your results with a questioning eye and ask yourself if they make sense.

Answer 15

143.3121019

Answer 16

which problem are you doing?

Answer 17

That's more like it...although not exactly what I got, and the problem does ask for the nearest 100th...

Answer 18

this is the 2nd problem

Answer 19

oh

Answer 20

143.31

Answer 21

What are you using for the value of pi?

Answer 22

calculator pi

Answer 23

Interesting. I get 143.239 using 3.1415926535

Answer 24

but 15 times 360 = 5400
12 times 3.14 = 37.68
5400/37.68=143.31

Answer 25

http://www.wolframalpha.com/input/?i=15*360%2F(12*pi)

Ah, but you are using 3.14, and those extra digits can make a difference, obviously.

Answer 26

okay well my calculator must stop at 3.14 cuz i get the same thing using calculator pi

Answer 27

Maybe it does. But here, punch in some extra digits and have a better chance of getting the right answer: pi = 3.141592

Answer 28

I'd hate to see you do the work correctly but get marked off just because your answer didn't round to the right digit in the 100ths place!

Answer 29

143.2394786

Answer 30

Right, now round that to the nearest 100th of a degree, as requested by the problem statement.

Answer 31

143.24

Answer 32

Yep, I believe that to be a true and correct answer for problem #2. Shall we try #3?

Answer 33

yes!

Answer 34

Great! I like sine curves :-)

Answer 35

You can draw nearly anything with the right combination of them!

\[y=-\sin(x-\frac{\pi}{4}) + 2\]

Answer 36

Let's do the easy part first. What does adding +2 to the function do to the graph?

Answer 37

adding +2 to the result of the function, that is

Answer 38

if we've got \(y = \sin x\) and we change it to \(y = \sin x + 2\) what happens?

Answer 39

my calculator is being stupid. should it move 2 spaces to the left?

Answer 40

@whpalmer4

Answer 41

Here, I'll be your human calculator :-)

x y = sin x y = sin x + 2
0 0 2
pi/2 1 3
pi 0 2
3pi/2 -1 1
2pi 0 2
etc.

Answer 42

so it moves by 2 each time

Answer 43

ok i got it now

Answer 44

gives us a vertical translation of 2

Answer 45

if we had subtracted 3 instead of adding 2, we'd have a vertical translation of -3.

Answer 46

okay!

Answer 47

Next, let's tackle amplitude. Amplitude is just the vertical scale of the function. Normally, the amplitude of the sine function is 1, because starting at y = 0, it goes to y = 1 and y = -1 as its most extreme values. written more precisely, if you have a function \(y = a \sin x\), the amplitude is given by \(|a|\).

Answer 48

So what is the amplitude of \(y = -\sin(x-\frac{\pi}{4})+2\) ?

Answer 49

It might be helpful to remember that \( -\sin x = -1\sin x\)

Answer 50

1

Answer 51

right!

Answer 52

:)

Answer 53

okay, we've done amplitude, we've done vert. translation, that leaves period and phase shift, which are trickier to grasp for many people (myself included). maybe you'll be an exception :-)

Answer 54

you know, before we do that, let's do the vertical translation and amplitude for the other half of the problem. \(y = 2 \cos 2\pi x\) what is the amplitude, and what is the vertical translation?

Answer 55

amplitude is 1 and vertical translation is 2

Answer 56

How did you arrive at those answers?

Answer 57

Oh, those are correct for the 1st equation, yes. How about the second equation, \(y = 2 \cos 2\pi x\) ?

Answer 58

oh oops sorry i though t you were asking what we already did above! Sorry!

Answer 59

No problem.

Answer 60

It would be a problem if you thought those were the answers for the second equation, however :-)

Answer 61

lol

Answer 62

would it be zero?

Answer 63

So, what do you think the corresponding answers for the equation \(y = 2\cos 2 \pi x\) are?

Answer 64

for amplitude, or vertical translation?

Answer 65

vertical translation?

Answer 66

is that an answer, or a prayer? :-)

Answer 67

a prayer lol

Answer 68

(my old math teacher loved that line, and so do I!)

Answer 69

vertical translation of 0 is correct.

Answer 70

lol its awesome! and im right?

Answer 71

FWIW, my goal is always to make anyone I help understand well enough that they answer with confidence.

Answer 72

yes, you are correct, vertical translation is 0. how about amplitude?

Answer 73

okay um hold on

Answer 74

is it 2?

Answer 75

yes? ;-)

Answer 76

what?

Answer 77

yes, the answer is 2. I was hoping you were certain about it :-)

Answer 78

lol :) yay im right!

Answer 79

great. now for the tricky stuff. sorry, the really, really, really easy stuff :-)

Answer 80

lol