Question

Solve each equation for 0le x < 2pi .
3cos ^{2}x -2cosx - 1 = 0
and the answer is 0, 1.9106, and 4.3726
I got the zero but how do I get the decimal numbers...

Answer 1

\[0\le x < 2\pi\]

Answer 2

is that ur anser

Answer 3

pardon me ?

Answer 4

the answer is 0, 1.9106, and 4.3726

Answer 5

u have the answer than why did u ask a question

Answer 6

I got 0. but I don't know how to get 1.9106 and 4,326

Answer 7

ow ok

Answer 8

can you factor your equation? what did you get?

Answer 9

show ur work
please

Answer 10

haha sure wait a sec

Answer 11

factored. (cosx-1)(3cosx+1).
so when cosx is 1 the solution for this is 0.
but when cosx is -1 over 3.. I am supposed to get the decimal number answers but I don't know how.

Answer 12

Are you in radian mode?

Answer 13

\[(\cos(x)-1)(3\cos(x)+1)=0\]
\[\cos(x)=1\implies x=0\]
\[\cos(x)=-\frac{1}{3}\implies x=\cos^{-1}(-\frac{1}{3})\]
then a calculator

Answer 14

then i get 1.9106...

Answer 15

yes i am in radian mode

Answer 16

yes thats importent i cep getting the rong answer till i put in the right mode

Answer 17

oh an since you are on the interval
\[[0,2\pi]\] you should add
\[\pi\] to the second answer

Answer 18

no sat she need to subtract her answer from 2pi

Answer 19

Well yes so you got 1.9106...
right?
what about the other value?
As sat and I were talking about the cosine will have this value twice, just look at the unit circle...

Answer 20

I don't know if I am supposed to subract that number by 2 pi or plus the number by pi

Answer 21

so say this is where the cosine is -1/3:can you find another spot that is also the same value of cosine?

Answer 22

oh plus 2 pi

Answer 23

another unit circle

Answer 24

well, 2pi-(this angle)the same value here occurs at 2pi-x

Answer 25

actually 2 pi - 1.9106 ?

Answer 26

right, look at the circle to see why...