Question

How do I graph this?
y=2-cos(2x+pi/2)

Answer 1

Can someone please explain how to do it manually ?

Answer 2

I need to know this for my final so please help me :(

Answer 3

\[y = A \cos(Bx+C) +k\]
A - amplitude, if A is neg it means graph is reflected about horizontal axis
B - determines period --> period = 2pi/B
horizontal shift , set bx+c= 0 --> x = -c/b
K - vertical shift

Answer 4

how to draw the graph in radians ?

Answer 5

do i start with the period first ? when I draw graph or what ?

Answer 6

well first determine amplitude --> A=-1 so its reflected and goes up/down 1 unit from axis

next find period... B = 2 --> period = 2pi/2 = pi
this means one cycle is completed in pi radians
divide by 4 to get increments
pi/4 , 2pi/4 , 3pi/4 , 4pi/4

2x+pi/2 = 0 --> x = -pi/4 this is horizontal shift to left

k = 2 this is vertical shift up 2

Answer 7

amplitude is -1 ?

Answer 8

since graph is shifted to left, start at -pi/4 then add increments

Answer 9

oh the coefficient in front of cos ok ok

Answer 10

yeah that ....technically amplitude can't be neg

Answer 11

oh ok, so the period determine when the graph end ? or stopped at ?

Answer 12

or complete is what i mean

Answer 13

right...horizontal shift tells you where to start....period tells you where to end and how big the increments are to each point

Answer 14

is there anyway that I can graph this in the calculator ?

Answer 15

yeah just plug in the function...any graphing calculator should be able to do it, make sure you are in radian mode

Answer 16

oh i see

Answer 17

hopefully he won't put any tricky answer on the test >.< cuz i am doom lol

Answer 18

but thanks for the helps @dumbcow :D

Answer 19

I will memorize the equation just in case >.<

Answer 20

hmm hold on, it seems like when i plug it in the calculator it show me the whole graph but it doesn't show me just one complete cycle ?

Answer 21

cow are you here ?

Answer 22

sorry yeah the calculator will graph the whole cosine wave, if you want to look at one cycle then you need to adjust the window so that range of x_values matches 1 period

Answer 23

you know how ?

Answer 24

in the original equation the "k" was not there, how did you know it was 2 ?

Answer 25

it was there, they just wrote it out of order
k is whatever the outside constant is

--> 2-cos(x) = -cos(x) + 2

Answer 26

oh so the 2 was k

Answer 27

what if it was -2 ? so the k is -2 ?

Answer 28

and that mean it shift down 2 units ?

Answer 29

then you shift the graph down 2

Answer 30

im just confuse on how to sketch the graph, like i dont know where to start first

Answer 31

what is all this pi/4, 2pi/4 stuff ? @@