Trigonometry: Solving for x in cos3x = 1/2

[bradyj7]

Hello,

I'm studying for an exam and am stuck on a trigonometry question. Could anybody help me out?

The question is:

Solve the equation cos3x = 1/2, for x is an element of R, (where x is in radians)

The answer is:

x = pi/9 + 2npi/3

or

x = 5pi/9 + 2npi/3

where n is an element of Z

Sincere thanks

John

My attempt

Well we know that cos (pi/3) = 1/2

But cos 3x = 1/2 and are trying to figure out what x is.

So what times 3 will give you pi/3. That would be pi/6.

3 * (pi/6) = pi/3

cos (3*(pi/6)) = 1/2

 

[genericusrnme]

If
'Well we know that cos (pi/3) = 1/2'
Then
cos 3x = 1/2
implies
3x=pi/3
implies
x=pi/9

 

[bradyj7]

Thanks,

It says that the answer is


x = pi/9 + 2npi/3

or

x = 5pi/9 + 2npi/3

 

[genericusrnme]

That is correct, when is Cos(a)=Cos(b)?