Question

How to graph y=3cos3x-2. I'm having some difficulties finding the intercepts

Answer 1

Amplitude = 3
Period = 2pi/3
2 units moving down

Answer 2

What shall I do next? @ganeshie8

Answer 3

Should I count by 1/4?

Answer 4

to find x-intercepts put y=0

Answer 5

3cos3x-2 = 0

cos3x = 2/3

Answer 6

you wanto solve this in (0, 2pi) ?

Answer 7

Yes

Answer 8

put 3x=t,

cos t = 2/3

Answer 9

solve t in (0, 6pi) and divide each solution by 3

Answer 10

Could you please further explain this bit

Answer 11

Pi,2pi,3pi, .....6pi?

Answer 12

And I divide each by 3?

Answer 13

sure :)

#First solution in \(t\):
\(\large \cos t = \frac{2}{3}\)
\(\large t = \arccos(\frac{2}{3}) = 0.841\)

Answer 14

lets first find all possible solutions in \(t\),
after that we can divide them by 3 to get solutions in \(x\)

okay ?

Answer 15

see if the first solution makes sense ? :)

Answer 16

Yes that will be 3x=0.84

Answer 17

So our first intercept will be x= 0.28

Answer 18

yup ! you got it !
but thats just one intercept. we need to find all other \(t\) values in (0, 6pi)

Answer 19

Sweet :)

Answer 20

use below to find two other \(t\) values :
\(\large \cos (t) = \cos(t + 2\pi)\)

Answer 21

So my next t will be ?

Answer 22

I go by 2pi?

Answer 23

yes for second solution : add 2pi to the first solution,

Answer 24

If so then it will be x= 2pi/3

Answer 25

for third solution : add 2pi to the second solution (which is same as adding 4pi to the first solution)

Answer 26

nope, u need to add 2pi to the first SOLUTION..

Answer 27

Ok. So I should go pi, 2pi, 3pi,etc

Answer 28

I'm confused

Answer 29

#First solution in \(t\) :
\(\large \cos t = \frac{2}{3}\)
\(\large t = \arccos(\frac{2}{3}) = 0.841\)

Second solution in \(t\) :
\(\large 0.841 + 2\pi \)

Third solution in \(t\) :
\(\large 0.841 + 2\pi + 2\pi\)

Answer 30

All the 3 solutions above ^^

Answer 31

Alright now I seem to get it

Answer 32

there will be 3 more,
but before that, see if the previous ones make sense :)

Answer 33

How do we know when to go by 2pi? Why can't we use pi?

Answer 34

very good question :)

\(2\pi\) is the period of \(\cos t\) function, so, its value REPEATS every \(2\pi\) units

Answer 35

I thought the period was 2pi/3

Answer 36

2pi/3 is the period of cos(3x)

2pi is the period of cos(t)

Answer 37

we had let t = 3x, to make the calculations easy

Answer 38

Ill try solve this tomorrow in the morning and will send you my answer :)

Answer 39

Thanks for your help. You are always amazing

Answer 40

sure.. take ur time ! good luck :)

Answer 41

no, you're amazing xD

Answer 42

Hi @ganeshie8

Answer 43

I tried but I just couldn't get it

Answer 44

Let us try graph y=sinx + 1

Answer 45

@ganeshie8