Question

How can I calculate the equation cos(xpi/6)=cos(xpi/4) for the smallest possible integer value?

Answer 1

Like this:
\[\cos(\frac{ x \pi }{ 6 })=\cos(\frac{ x \pi }{ 4 })\]
Where x = smallest positive integer

Answer 2

@asnaseer This is actually a follow up question to my previous one :P

Answer 3

@wio Can you help me with this?

Answer 4

@AravindG ?

Answer 5

@ash2326 ?

Answer 6

can you post a quick screenshot of the material?

Answer 7

maybe there's something we're missing from the exercise

Answer 8

No there isn't anything missing, is there something wrong with the equation? I know the answer, I just don't know how to get it.

Answer 9

Oh there's a typo in the question - it should be smallest positive integer, not smallest possible integer

Answer 10

You could approach it as follows:
\(\cos(\theta)=\cos(2\pi n+\theta)\) for \(n=1,2,...\)
\(\therefore\cos(\pi x/6)=\cos(2\pi n+\pi x/6)=\cos(\pi(12n+x)/6))\)

We therefore need to solve:
\(\cos(\pi x/4)=\cos(\pi(12n+x)/6))\)
i.e.:
\(\pi x/4=\pi(12n+x)/6\)
which leads to:
\(x=24n\)

So the smallest positive \(x=24\)