Question

Solve:

cos(x/4)=1/sqrt(2)

It's been a while since I have done this stuff, can anyone help me, or atleast give me a hint?

Thanks in advance.

Answer 1

\[\cos(\frac{x}{4})=\frac{1}{\sqrt{2}}\]

Answer 2

At what angle cos becomes 1/root(2) ??

Answer 3

45

Answer 4

Yes so:

\[\cos(\frac{ x}{4}) = \cos(\frac{\pi}{4})\]

So what can be x here???

Answer 5

Oh Cool, that means x must be pi, that helps a lot, thanks ^_^

Answer 6

Welcome dear...

Answer 7

Are you looking for the general solution of this??

Answer 8

No thanks, just the solutions between -2pi>x>2pi, but there is only two solutions.

+/- pi :)

Thanks, I may have another shortly :)

Answer 9

It is true that one value of x is \( \pi\) but there can be more values of x..

Answer 10

For knowledge I will tell you more that :

For \(cos \theta = cos \alpha\) the general solution is given by:

\(\theta = 2n \pi + \alpha\), where \(n\) is an integer...


So for this question:

\[\cos(\frac{x}{4}) = \cos(\frac{\pi}{4}) \implies \frac{x}{4} = 2n \pi + \frac{\pi}{4}\]

\[\large \implies x = 8n \pi + \pi\]

Put n = 0 here you will get: \(x = \pi\)

Similarly put n = 1, 2 or -1, -2 you will get infinite values for x...

Answer 11

I know, I'm only looking for the solutions between -7>x>7 on the x axis. Thanks anyway :)

Answer 12

Welcome dear..