Question

Solve the equation on the interval (0, 2pi): 12 cos^2 x-9=0

Answer 1

isolate the cos^2(x) first

Answer 2

ok so cos^2=9/12
cos^2=3/4?

Answer 3

ok you mean cos^2(x)=3/4
cool

Answer 4

now take square root of both sides and you will have two equations to solve

Answer 5

ok ummm hold on

Answer 6

cosx=sqrt3/2?

Answer 7

plus or minus

Answer 8

you have
\[\cos(x)= \pm \frac{\sqrt{3}}{2}\]

Answer 9

\[\cos(x)=\frac{\sqrt{3}}{2} \text{ or } \cos(x)=\frac{-\sqrt{3}}{2}\]
we need to solve both of these equations
a good place to start is looking at the unit circle

Answer 10

ok

Answer 11

pi/6?

Answer 12

and 5pi/6?

Answer 13

\[\cos(x)=\frac{\sqrt{3}}{2} \text{ has solutions } x=\frac{\pi}{6} \text{ or also what ?} \\ \cos(x)=\frac{-\sqrt{3}}{2} \text{ has solutions } x=\frac{5\pi}{6} \text{ or also what ? }\]

Answer 14

there are two more solutions
one for each equation above

Answer 15

11pi/6 and 7pi/6?

Answer 16

\[\cos(x)=\frac{\sqrt{3}}{2} \text{ has solutions } x=\frac{\pi}{6} \text{ or } x=\frac{11 \pi}{6} \\ \cos(x)=\frac{-\sqrt{3}}{2} \text{ has solutions } x=\frac{5\pi}{6} \text{ or } x=\frac{7 \pi}{6}\]

Answer 17

yep! :)
good job

Answer 18

yay! so thats my answer?

Answer 19

but what about the part where is says on the interval 0, 2pi?

Answer 20

There are no more solutions in that interval.
We already found them all.

Answer 21

ohhhhh!! thank you! omg thank you so much!!!!