Question

y=1/2 cos (3x+3.14/2) need help not sure how to do it.

Answer 1

@jim_thompson5910

Answer 2

Data_LG2 you can't distribute like that

Answer 3

why?

Answer 4

because cos isn't being multiplied out front

cos is a function

Answer 5

oh ok, sorry.. i'll try again

Answer 6

@jim_thompson5910 do we need to use identities here?

Answer 7

yes but that is not what i'm suppose to do. I forgot to look at the directions for this problem I just wrote it down. I think it is a vertical shift. and I have to graph it also. sorry I should have told y'all.

Answer 8

you could use identities, but acegirl may just want to graph this or figure out the period/phase shift

Answer 9

oh transformations????, i thought we need to solve it

Answer 10

In general

y = A*cos(Bx - C) + D

has an amplitude of |A|

has a period of T = 2pi/B

has a phase shift of C/B (this is the horizontal shift)

and D takes care of the vertical shift

Answer 11

@jim_thompson5910 that's what i'm working with

Answer 12

so in this case, what are A, B, C, D?

Answer 13

amp=1/2
period=2pi/B=2pi/3
p.s.=C/B=pi/2/3
not sure how to work that out

Answer 14

@jim_thompson5910

Answer 15

amplitude and period are correct

Answer 16

phase shift

C/B = (-pi/2)/3 = (-pi/2)*(1/3) = -pi/6

so this means you shift the graph pi/6 units to the left

Answer 17

the original graph of cos(x) has not been shifted vertically to get 1/2 cos (3x+pi/2) since D = 0

Answer 18

where did you get the negative pi from?

Answer 19

well notice the form I'm working with is y = A*cos(Bx - C) + D

pay particular attention to the -C

Answer 20

okay

Answer 21

y = 1/2 cos (3x+pi/2)

is the same as

y = 1/2 cos ( 3x- (-pi/2) ) + 0


now compare that to y = A*cos(Bx - C) + D

and we see that

A = 1/2
B = 3
C = -pi/2
D = 0

Answer 22

okay

Answer 23

hopefully all that makes sense

Answer 24

so is the phase shift pi/6?

Answer 25

units to the left

Answer 26

yes

Answer 27

If C is negative, you shift left

If C is positive, you shift right

Answer 28

yes it does and thank you.
@jim_thompson5910

Answer 29

ok glad it does, yw