Question

5cos2(theta)=2
Find all solutions in interval [0,2pi)

Answer 1

so
cos2(theta)=2/5
2(theta)= ?

Answer 2

@peachpi it's a little different.. :P

Answer 3

Is that cos 2Θ or cos² Θ?

Answer 4

the first

Answer 5

ok. so the first thing I like to do when Θ is multiplied is "fix" the interval.
0 ≤ x < 2π
Since the x is multiplied by 2, multiply the whole interval by 2 to get
0 ≤ 2x < 4π

Answer 6

so we do the same thing we did last time, except now we're looking for solutions from 0 to 4pi.

cos 2Θ = 2/5
2Θ = arccos (2/5)

Answer 7

arccos(2/5) = 1.159
so we want to add pi to this?

Answer 8

or, sorry, subtract this from 2pi

Answer 9

You want to divide that by 2
Θ = ½ arccos (2/5) → answer in 1st quadrant on the interval from 0 to 2pi
Then add 2pi to get the 1st quad angle between 2pi and 4pi

Answer 10

em so the original answer is
0.579
adding 2pi = 6.862

Answer 11

the 0.579 is right. and you actually subtract it from 2pi to get the other answer

Answer 12

so 5.7

Answer 13

*5.8 :)

Answer 14

Yes. 5.8 :)
There are going to be two more solutions. You got 2Θ = 1.159. Add 2pi to that, then divide by 2 to get the corresponding Θ.

Answer 15

should get 3.72

Answer 16

Yep yep

Answer 17

and then (2pi - 1.159)/2 for the 4th solution is 2.56

Answer 18

K so it's
theta = 1.159/2
= 0.579

So our first answer: 5.8
add 2pi to that: 3.72

next we have 2pi-0.58 = 5.70 (our third answer)
then 5.70 - pi = 2.56 (our fourth answer)

haha sorry that's all jumbled up.

Answer 19

= 0.58, 3.72,5.70,2.56

Answer 20

yep

Answer 21

I'll get this. Sometime.
thanks!

Answer 22

you're welcome

Answer 23

@peachpi I just did one by myself!! and got the right answer! xD :')

Answer 24

awesome!