Question

State the amplitude, period, phase shift, and verticle translation for y = -sin(x-pi/4)+2

Answer 1

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

Answer 2

@TeresaCal Last trig function problem, thanks a ton for the help on the last one :)

Answer 3

The general formulas for sine and cosine are y = Asin(Bx C) + D and y = Acos(Bx C) + D.

We shall begin by labeling the various components.

A amplitude of the function = (max-min)/2 (vertical stretch of the graph)
B stretch/shrink on the x-axis. (It compresses or expands the graph.)
C/B the phase shift of the graph (the shift left (if C/B is neg.) or right (if C/B is pos.))
D the vertical shift of the graph.

Answer 4

Starting with amplitude, A = 1 correct?

Answer 5

Anything before "sin" is included with A. So A = -1

Answer 6

Alright, now B. B = 1 right?

Answer 7

I would assume 1 just takes the place considering there is nothing there. Sorry, I'm not used to seeing functions set up like this.

Answer 8

Yes, B = 1 in this case

Answer 9

Okay, and I know to find the period it is 2pi/B so in this case, the period is simply 2pi correct?

Answer 10

Correct again

Answer 11

Excellent, now for the phase shift. Would the answer for phase shift be written simply as "pi/4 units to the right"?

Answer 12

Sounds about right :)

Answer 13

Alrighty and vert shift is 2 units up of course

Answer 14

Hang on...

Answer 15

Oh wait, phase shift would be horizontal compression right?

Answer 16

No, don't get those two things confused.

Answer 17

Phase Shift is C/B

In this case, B = 1 so C/B = pi/4

Answer 18

If B was anything other than 1, then the phase shift would be different from the horizontal compression

Answer 19

Only when B = 1 does phase shift = horizontal compression

Answer 20

Okay okay :) One of the trickiest parts for me is keeping the whole horizontal/verticle compression and stuff.

Answer 21

Well that just about does it @Hero Thank you so much for all the help and I wish I could give more medals!

Answer 22

One medal is good enough, thanks :)