Wave equation derivation Why is the angle assumed to be small?

[McLaren Rulez]

http://www.math.ubc.ca/~feldman/apps/wave.pdf is the link from where I understood how to derive the wave equation. But why is theta assumed to be small? As I understand it, theta is the angle that the string segement we're considering makes with the horizontal. Even a simple sine wave seems to form pretty reasonable angles with the horizontal. So what's my misconception here? Thank you

 

[The_Duck]

Depends on the amplitude of the sine wave. The simple wave equation won't be quite correct for large-amplitude oscillations, which will make the system non-linear (waves won't pass through each other unscathed as they do with the simple wave equation).

 

[McLaren Rulez]

So essentially, the assumption is that the amplitude of oscillation is small. Thank you for clearing that up.