all possible angles of a trig ratio

is there a methodical way to find all the possible angles of a given trig ratio? (Thinking)that is a regular method of working through all the known laws of that ratio (such as sinA= (pi - A) or -sinA = (2pi - A))? personally i often get tangled up in these properties and am constantly turning up with the same or negative angles.(Angry)

General Solution of trig equations

Hello furor celtica Quote:

Originally Posted by

**furor celtica** is there a methodical way to find all the possible angles of a given trig ratio? (Thinking)that is a regular method of working through all the known laws of that ratio (such as sinA= (pi - A) or -sinA = (2pi - A))? personally i often get tangled up in these properties and am constantly turning up with the same or negative angles.(Angry)

Yes, there is. This is it!

For , what you need is the general solution of the equation , and it is:

So, for example, if (which is pretty obvious)

Then if (which means that , which I'm sure you knew.)

If (so )

If , and so on.

So you can find, for example, the general solution to the equation , as follows:

We know that , so we need to solve . Using the above formula, the general solution is:

For the corresponding result is:

has the general solution

Put some values in for , as I did above, and you'll see how it works.

Finally,

I think you'll find that answers your question without reference to any diagrams.

Grandad