# Trig General Solutions

• Jun 5th 2009, 04:48 PM
xwrathbringerx
Trig General Solutions
Hi

For tan x = sin x, why is the general solution only x = pi*n and not also x=2pi*n?

Similarly, for cos (3x) = cos (x), why is it only x = pi*n/2 and not also x = pi*n?

Thanx!
• Jun 5th 2009, 05:01 PM
mr fantastic
Quote:

Originally Posted by xwrathbringerx
Hi

For tan x = sin x, why is the general solution only x = pi*n and not also x=2pi*n?

Similarly, for cos (3x) = cos (x), why is it only x = pi*n/2 and not also x = pi*n?

Thanx!

In both cases the second solution you state is a subset of the first eg. $\displaystyle x = 2 \pi n$ is a subset of $\displaystyle x = \pi n$ where n is an integer.

Write out some of the concrete solutions that both expressions give and you will see this.
• Jun 5th 2009, 05:05 PM
xwrathbringerx
Hey is it alrite to write both as solutions i.e. x = .... or ..... OR do i hav to just write the 1st solution?
• Jun 5th 2009, 05:08 PM
mr fantastic
Quote:

Originally Posted by xwrathbringerx
Hey is it alrite to write both as solutions i.e. x = .... or ..... OR do i hav to just write the 1st solution?

Well, writing both is not wrong so I doubt you'd be penalised in an exam. But if you can recognise that one general solution is a subset of another, you'll have a more elegant answer.

But if in the slightest doubt, you should always write both.