# Question:Finding all solutions to 2 simultaneous trigonometric equations in a given interval

## Question:Finding all solutions to 2 simultaneous trigonometric equations in a given interval

Maple 2015

Hey there folks - I have the following headcracker...

I have 2 equations:

cos(a t) = cos(b t + c)
&
sin(a t) = sin(b t + c)

Where a, b and c are known constants, and t is a variable.

I would like to find a way to solve these 2 equations simultaneously, i.e. find the t values that solve both equations at the same time. Of course, there will be an infinite number of solutions, so I also need a way to define an interval that t needs to be restricted to, e.g. t = 0..20 * Pi .

The best I've managed is:

... but I can't seem to make this work for solving the 2 trig. equations simultaneously

nor can I figure out the syntax for getting all solutions compiled as a list, e.g.

- which would be enormously helpful for further calculations.

Can anyone give some help on this?

Regards,  Matthew

﻿