Question

find all values of ������ betwen 0 and 4 such that 4cos(2pi������)=3

hey zepdrix...can you see me???

Answer 1

Hey Dawn c:

\[\Large\rm 4\cos(2\pi \theta)=3,\qquad\qquad 0\le\theta\le4\]So we need to find some angles huh?
Hmm

Answer 2

Dividing by 4,\[\Large\rm \cos(2\pi \theta)=\frac{3}{4}\]Applying the inverse cosine gives us,\[\Large\rm \cos^{-1}\left(\frac{3}{4}\right)=2\pi \theta\]Dividing by 2pi gives us,\[\Large\rm \frac{\cos^{-1}\left(\frac{3}{4}\right)}{2\pi}=\theta\]This will give us our FIRST angle between 0 and 4.

Answer 3

Are you sure the cosine isn't being squared?
The problem works out a lot nicer if it is D:
If not, that's ok. Just have to rely on the calculator then.

Answer 4

Dawwwwn XD Where you at!

Answer 5

i'm here, can you see me now?

Answer 6

Oh maybe it's fixed now c:

Answer 7

this is what I did:

cos(2piθ) = 3/4
2πθ=cos-1(3/4)
θ=cos-1(3/4) / 2π
θ=1.135

but evidently that's not the right answer...

no, the cos isn't squared...sorry...

Answer 8

so i did the first part right i guess, did i just have it in the wrong form? the question says to "round your answers to the nearest thousandth...

Answer 9

Theta is between 0 and 4
The units are very clear.
This is 4 radians or degrees?
I guess radians would make sense..

Answer 10

units aren't*

Answer 11

that's what i thought too seeing as how i have to have the answers to the nearest thousandth...

Answer 12

sec >.> thinking

Answer 13

i'm thinking that may i need to add the period or something? but do inverse functions have periods?

Answer 14

How did you get 1.135?

cos-1(3/4) / 2π = 0.115
when I put it into the calculator ^

Answer 15

Ohh I see.. you gotta be careful with your calculator.

Input it like this:
\[\Large\rm \cos^{-1}(3\div4)\div(2\pi)\]If you don't put brackets around the 2pi, it will instead interpret the problem like this:

\[\Large\rm \frac{\cos^{-1}\left(\frac{3}{4}\right)}{2}~\pi\]

Answer 16

got it, now i'm with you...

Answer 17

am i on the right track with the period? should I be adding that? or do inverse functions not have periods?

Answer 18

Period? :O
I'm not sure what you mean.

It's a decimal value, so yes it should have a decimal.

Answer 19

no, i mean the period of the wave/graph

Answer 20

Oh lol :D

Answer 21

Yes, we need to deal with adding to find the other angles.
The inverse function only gives us the first angle, it doesn't give us the other coterminal angles between 0 and 4. But we still need to look for them :d so yes.

Answer 22

ok, i think i can get it from here. thanks so much for your help!! i have a lot more to do, is there a way i can ask you questions directly?

Answer 23

The other angles might be a little tricky to find.
Yes, you need to add the period to get the first set of solutions...
but there is another set of solutions!

Remember in trig that you get two angles corresponding to one value.

Example:\[\Large\rm \cos(2\pi x)=\frac{\sqrt3}{2}\]This would tell us that:\[\Large\rm 2\pi x=\frac{\pi}{6}+2k \pi\]But this is only the first set of solutions.
The other angle corresponding to this sqrt3/2 is:\[\Large\rm 2\pi x=\frac{11\pi}{6}+2k \pi\]You could find this other set of values by subtracting the first angle from the period.\[\Large\rm \theta_1=0.115\]\[\Large\rm \theta_2=1-0.115\]Then you can add 1 to those (your period) to find the other angles.
But getting that second SET of angles is a little tricky :O I just wanted to make sure you understood that part.

Answer 24

Directly? No.
The website has been really wonky lately :c hard to respond.

Close this thread and open a new one when you're ready to post a new question. In the comments you can put @zepdrix or @someelse who is in the lobby area. It will send a page to me/them, so it's easier to find your question on the list.

Answer 25

ok, i'll try that! thanks again!! :)