Question

State the period, amplitude, max/min values, range, domain, horizontal phase shift and vertical displacement.
y= 2cos(-1/2x +90^@)-3

Answer 1

You should get to it. Where do you plan to start?

Answer 2

simplifying it first

Answer 3

can you do it for me?

Answer 4

I don't think so. The point of this exercise is that it is as complicated as possible. You may wish to factor the stuff inside the argument of the cosine function.

Answer 5

can you just put this equation in the form of y = a sin[b(x - c)] + d

Answer 6

stop making it so complicated

Answer 7

are you there?

Answer 8

Observation #1 - You are asking for help.
Observation #2 - The fact that you are asking for help suggests you need help.
Rule #1 - The Code of Conduct prevents just doing it for you. I can't be in your exam!
Rule #2 - A volunteer trying to help you gets to pick HOW to help you.

I already told you to factor the stuff in the argument of the cosine. Do that. This is not only to solve the problem, but also to prove that you have sufficient algebra skills so that you can be expected to be able to solve the problem.

You have \(-\dfrac{1}{2}x + 90º\). Factor out -1/2 and the entire expression will be in the desired form.

Answer 9

Then you are saying that you do not know how to factor out the -1/2? That's all it takes. You can do it. I am nearly certain.

Answer 10

ok I factored it

Answer 11

Show the factoring, please.

Answer 12

at least tell me if its right ?

Answer 13

Show it and I will.

Answer 14

y= 2cos(-1/2(x-180^@))-3

Answer 15

That's pretty good. Excellent work.

Okay, here we go.

y = cos(x)

Period: 2pi
Amplitude: 1
Range: [-1,1] <== Min and Max
Domain: All Real Numbers
Phase Shift: None
Vertical Shift: None

Do you believe all that?

Answer 16

ok Thank you

Answer 17

That's just the beginning. The unaltered cosine function. We have not yet approached your problem statement.

Answer 18

do you want to help me with a new question ?

Answer 19

are you there?

Answer 20

Haven't done the old one, yet.

Answer 21

its fine thats all I need

Answer 22

Well, then, excellent! Since you did it yourself.

Answer 23

yes

Answer 24

ok this is the next one that I need help with: The graph of y = -3sin( 2x) is shifted to the left by 30 units and up 5 units. Write the new equation.

Answer 25

Up is easy. Add "+5" on the end.

Answer 26

left and right are a little trickier. Shall we use +30 or -30?

Answer 27

so it would be y= 3sin(2x) +5 ?

Answer 28

-30?

Answer 29

No, sorry, that will move it right. It's a little counter-intuitive.

We just need to play with the argument.

We have

(2x)

It would be a mistake to write

(2x + 30)

You tell me why.

Answer 30

it would give you the horizontal translation instead

Answer 31

No, we what a horizontal translation of 30.

(2x + 30) is a horizontal translation of only 15.

Remember that factoring? (2x+30) = 2(x+15)

To achieve a left shift of 30, we must use [2(x+30)]

Answer 32

+5 then?

Answer 33

We already did that. Out on the end that is a vertical shift of 5.

Inside the argument cos(2x) vs. cos(2(x+30)) is a left shift of 30

Answer 34

ok what is the full equation ?

Answer 35

You have the first half.

y= 3sin(2x) +5

Add the other piece.

Answer 36

[2(x+30)] ?

Answer 37

That's the piece.

y= 3sin(2(x+30)) +5

Done.

Answer 38

thank you !

Answer 39

No worries. Glad we could get along.

Answer 40

I have another one

Answer 41

Describe how the graph of y+3 = 2sin (3x+90^@) compares to the graph of y = sin(x)

Answer 42

Two things to prepare:

1) Move that 3 off the y. It needs to be on the other side to be in standard form.
2) Yet another time, factor that argument.

Answer 43

ok so the 3 would become -3

Answer 44

Right. And the factoring?

Answer 45

ok I got it !

Answer 46

My answer: y= 2sin(3(x+30^@))-3 ??

Answer 47

BTW to get the degree symbol, hold down your [alt] key, and while holding it down, type on your numeric keypad 0 1 8 6.

Answer 48

Not quite an answer, but it is now in standard form.

Answer 49

ok thanks
so its not right?

Answer 50

If you want it in standard form, you are done.
If you wish to describe how it is different from sin(x), you have only just begun.

Answer 51

No I need to describe it to sin(x) how do I do that?

Answer 52

Then do that. What are the four pieces?

y= 2sin(3(x+30^@))-3 ??

'2' in front does what to the amplitude?
"-3" in the back does what to the vertical?
"3" in the argument does what to the period?
"+ 30º" in the argument does what to the phase shift?

Answer 53

but thats the equation I had

Answer 54

There is no objection to the equation. What do all the parts do? This is the question.

gtg Good luck.

Answer 55

oh ok

Answer 56

what are the functions of sin(x)