- #1

- 43

- 6

"If (theta) is small, sin(theta) may be replaced by [partial]dy/dx."

I expected to see sin(theta) = (theta) so this threw me off. This came up in the derevation of the one dimensional wave equation after approximating (by Taylor series) the transverse force on a mass element of a tensioned string with [partial]d(Tsin(theta))/dx. The approximation in question thus gave T*([partial]d2y/dx2)*dx.

In the original setup, x and y are cartesian axis in physical 2D space and (theta) is the angle the string (with tension T) makes from the x-axis after displacement from equalibrium.

I've never seen sine approximated by dy/dx before and was hoping somebody might shed some light for me :)