Question

y=-sin(x-pi/4)+2
amplitude, period, phase shift, vertical translation, graph the function
I know the amplitude=-1 and vertical translation=up 2 but I don't know how to find period or phase shift

Answer 1

Hi,
\(\huge\color{yellow}{{Welcome~To~Open~Study}!!!!!!}\)

Answer 2

What do you think it is?

Answer 3

well amplitude is -1
vertical translation is up 2
right?

Answer 4

@iGreen

Answer 5

or would amplitude be a positive number

Answer 6

amplitude would be positive.. because it is distance so amplitude=1

Answer 7

The standard form of a trig function is a*(trigfunction)(bx + c) + d

Answer 8

see
http://www.intmath.com/trigonometric-graphs/3-graphs-sin-cos-phase-shift.php
for a quick summary

Answer 9

a is amplitude for sin and cos
b helps find the period (2pi/b = period)
c is the phase shift
d is the vertical shift

Answer 10

so phase shift would be pi/4/1

Answer 11

b is -pi/4
Period is (2pi)/(-pi/4)

Answer 12

Whatever that simplifies to

Answer 13

is it 8?

Answer 14

@phi

Answer 15

\[ y=-\sin\left(x-\frac{\pi}{4}\right)+2 \]
match that up with
\[ y = a \sin (bx + c) \]
amplitude is the |a| or 1 (this means the sin moves up and down by 1 (total distance from the top to the bottom is 2)

to find the period, match b with 2 pi/ T, where T is the period. b is 1 here, so
\[ 1 = \frac{2 \pi}{T} \\ T = 2 \pi \]

the period is 2 pi

the phase shift is -c/b
c is -pi/4 and b is 1 so you get
phase shift = \( - \frac{- \pi}{4} = \frac{\pi}{4} \)

Answer 16

ok. so for this problem: y=1/2cos(2x)-1
amplitude=1/2
vertical translation= down 1
period= pi
phase shift=0
is this correct?

Answer 17

@phi

Answer 18

yes, your answers for the cos problem look good.

btw, for the -1 * sin(x - pi/4)
they may want us to rewrite it as
1 * sin (x - pi/4 + pi) which can be written sin(x + 3 pi/4)
(in other words, the -1 can be thought of as causing a phase shift)

Answer 19

thank you so much! and i need to graph these i can just put it in my calculator right?
Y= -sin(x-pi/4)+2
and Y=1/2cos(2x)-1
and i enter it into the calculator just like that right?

Answer 20

@phi