Question : solving trig equations - multiples of pi in the answer

Hi

Lets say you are solving a trig equation of the form acosx + bsinx using Rsin(x + theta) and you get your answer to be something like

x = pi/2 - theta +/- n*2*pi

and then you can find out tan(theta) is 0.75 so that theta is 0.64  +/- n*pi rad

How do you then link these 2 answers together as you have have plus/minus multiples of pi or 2pi in both parts of your answer. If its correct to give multiples of pi for the x part of the answer then surely its correct to also give multiples of pi for the theta part of the answer?

The whole question was just to solve 3cosx + 4sinx = 5

thanks

Answer : solving trig equations - multiples of pi in the answer

It is correct, but not useful. For example, if you need to solve sin(x)=0.5, you find that x=pi/6 is a solution, and it's usually sufficient. Formally, the solution is x=pi/6+n2pi, n being any natural number (with negatives), just like you suggest for theta.

The goal is to find all solutions for x, so the correct answer must include them all. You do not need or want to find all possible values for theta. One value is enough, and you choose the one that is most readable.

Does that answer your question, or did I miss your point entirely?
(°v°)