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
Yes, there is. This is it!
Originally Posted by furor celtica
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.
I think you'll find that answers your question without reference to any diagrams.