Question

solve the equation for principal values of X. Express solution in degrees cos x= 3cos x-2

Answer 1

\[2\cos(x)-2=0\] is a good start

Answer 2

can you put some parentheses in so the eq is clear please

Answer 3

that was whats on the worksheet hun

Answer 4

so next it would be 2 cos x= 2?

Answer 5

yes

Answer 6

I'm sure there are some parentheses around the inside of the cosine, ie is it cosine(x-2) or is it cos(x)-2

Answer 7

and then divided by two?

Answer 8

so cos x=1?

Answer 9

so im confused dose x= 0, 180, 360, or 540 degrees?

Answer 10

cos(180)=-1 not 1
cos(540)=-1 not 1

Answer 11

so its 360 or 0?

Answer 12

well there are infinitely many solutions

Answer 13

also what does principal values mean here?

Answer 14

yea i got that but my teacher wants one

Answer 15

i have no idea, that's one of the reasons Im confused

Answer 16

can't help you if you don't tell me what principal values mean

Answer 17

it is probably 0 though

Answer 18

a principal value is a value along one branch of the function. but ill go with 0

Answer 19

@misty1212 what the heck does that definition mean?
what is a branch of a function?

Answer 20

haha 0 was correct i checked with my older brother no worries

Answer 21

I still want to know what branch of a function means

Answer 22

lol

Answer 23

its a branch of a function. if you graph a function a piece between two points on the graph would be a branch of the function, at least that's how i would look at it logically then again math is rarely logical

Answer 24

Well it is definitely suppose to be logical.
But I think you meant this for the definition of principal values:
For sin(x)=a, it is a number x between -90 deg and 90 deg (including endpoints).
For cos(x)=a, it is a number x between 0 and 180 deg (including endpoints).

Answer 25

probably means the answer on the interval
\[[0,2\pi)\]

Answer 26

so in this case you pick \(x=0\)