# Trigonometric Equations

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

Peter G.

Last edited:

SteamKing
Staff Emeritus
Homework Helper
What can you say about what sin (0), sin (180) and sin (360) have in common?

All of them are equal to 0.

SteamKing
Staff Emeritus
Homework Helper
So, could any of those angles satisfy the original equation?

eumyang
Homework Helper
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)).

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