How can I find angles that satisfy 3sin(2x) = sin(x)?

[Peter G.]

Hi,

3sin(2x) = sin (x)

I managed to find two answers: 80.4 Degrees and 279.6 degrees but I don't know hot to get 0, 180 and 360 as answers, can anyone help me?

This is how I found the two other angles:

6 sin (x) * cos (x) = sin (x)
cos (x) = sin (x) / 6 sin (x)
cos (x) = 1/6

Thanks in advance,
Peter G.

 

[SteamKing]

What can you say about what sin (0), sin (180) and sin (360) have in common?

 

[Peter G.]

All of them are equal to 0.

 

[SteamKing]

So, could any of those angles satisfy the original equation?

 

[eumyang]

Hi,

3sin(2x) = sin (x)

I managed to find two answers: 80.4 Degrees and 279.6 degrees but I don't know hot to get 0, 180 and 360 as answers, can anyone help me?

This is how I found the two other angles:

6 sin (x) * cos (x) = sin (x)
cos (x) = sin (x) / 6 sin (x)

You shouldn't have divided both sides by sin(x). You lose potential solutions that way. Instead, subtract sin(x) from both sides and factor out the greatest common factor (sin(x)).

 

[Peter G.]

Hi,

Thanks guys. With my teacher and your input, I understood what I did wrong:

6 sin (x) * cos (x) = sin (x)
6 sin (x) * cos (x) - sin (x) = 0

sin (6cos(x) - 1) = 0