What a sine curve look like?

Answer 1

A sine curve/sine wave looks like a long half moon with another running over it starting in approximately the middle of the first and continuing. Wish I could draw how it looks on an oscilliscope Draw a long mound on a paper several times connected together. The go back to the first mound and start the same mound line in the middle of the first and loop over the next,etc.etc

It looks like a circle that is bisected into 2 semicircles, then had the top semicircle rotated 180 degrees such that both semicircles are connected at only one point.

Aaarrghhh!

You can plot it using a construction based on a circle divided into segments, from the intersections of radii and circumference. Alternatively plot it as amplitude against angle using a scientific calculator or sine table: for one complete cycle of the wave the turning-points are 1 and -1 at 90 and 270 degrees respectively, it equals 0 at 0, 180 and 360 degrees.

Or use Excel!

It does NOT look like 2 semicircles at all! It is not a set of circular arcs! The curve starts concave, becomes almost straight for an infinitesimal section then goes convex as it approaches the turning-point.

Simple ripples on a pond, or deep ocean swell unaffected by local wind, follow the same form.