General solutions

Hi there! is there any clarification on what the general solution does. I am finishing assessments without using it and i feel as though i’m missing some steps

Hi alexlivingstone
A general solution allows you to put in values of ‘n’ to get many solutions for an equation instead of just one (which is a ‘particular solution’). Because trig graphs repeat over and over, you can’t write every solution down (if you are given values of x between which the solutions lie you can give every answer between those values). The general solution allows you to create a formula that would enable you to find any solution.

ahh right thank you. so in an assessment i would find the exact solution using the information provided (by setting my model equal to whatever y value) and then i would go on to find the general solution? how do I provide evidence that my general solution works?

You can confirm your trigonometric model using your graphic calculator, Desmos or Geogebra it see the pattens and using the properties of the sine, cosine or tangent functions from the principal values found within one cycle then add the multiples of the period to these to get the general values or use the general solution formula on the a NZQA Formula Sheet.