multiple solutions to equations involving sine
i'll get straight to the problem
i'm looking for non-numerical, non-iterative methods for finding the solutions to equations such as this:
sin(pi*2^x) = sin(pi*2^(1-x)) = 0, over the range [-1 < x < 2]
in words, i'm looking for where the given functions simultaneously intersect each other and the x-axis
sin(pi * 2^x) = 0
sin(pi * 2^(1-x)) = 0
pi * 2^x = c1 * pi
pi * 2^(1-x) = c2 * pi
where c1 and c2 are integers >= 0
2^x = c1
2^(1-x) = c2
..ok so clearly i'm just transforming this a little to see if i jog someone's memory
i vaguely remember something in calculus that would lead to multiple solutions..however it somehow involved integrals..does anyone know what those types of calculus equations are called? how to solve them?
oh can't calculus find the points of intersection of a parabola and a line? can i use a similar process on my equations?