Question

How do I find all possible values for Ɵ in the equation cos 4Ɵ = 0 ?

Answer 1

cosx = 0 implies x = (2n+1) * pie/2 ............... hope nw u can find for cos 4x

Answer 2

if i know that cos θ = 0 at \[\frac{ \pi }{ 2 } and \frac{ 3 \pi }{ 2 }\] then can i use this information to get the answer @Yahoo! ?

Answer 3

What if those angles were 1/4 as big?

Answer 4

so i should multiply those by 1/4 and those are the values for that equation?

Answer 5

Well, if 4 times ? = one of those angles, wouldn't it follow that 4 times ? would satisify cos 4 theta = 0?

Answer 6

Of course you realize you cannot really find ALL the valuse because cos theta is periodic, so the value recur as you go around the unit circle over and over.

Answer 7

well when i enter cos 4 θ = 0 into mathway.com, i get \[\frac{ \pi }{ 8 } \pm \frac{ \pi n }{ 2 } , \frac{3 \pi}{2} \pm \frac{\pi n}{2}\] I'm not sure where the πn comes from.

Answer 8

Okay, I misspoke there. If you know the values that satisfy \( \cos\theta = 0 \) then sure 1/4 of those values would satisfy \( \cos 4 \theta = 0 \). But you seem to have got it anyway.

Answer 9

The unit circle is \( 2\pi \). Every time you go around it you get the same value. so if x is a solution, \(2\pi + x \) is a solution and so is \(4\pi + x \) and \(6\pi + x\) and so forth. So \(2n\pi + x\) is the a solution for integers n (except integer 0).

Answer 10

I see, though why is it also divided by 2?

Answer 11

I think that should be:

\(\large\frac{ \pi }{ 8 } \pm \frac{ \pi n }{ 2 } , \frac{3 \pi}{8} \pm \frac{\pi n}{2}\)

because of the plus/minus, it is telling you that it is true for n=1, 2, 3, ...

Answer 12

ok, it makes more sense with it being as you just put than with 3π/2

Answer 13

Thank you for the help.

Answer 14

Sure.