Let's have a curve C. Vary two tangents to the curve in such a way that the angle between the two lines is a constant. Then the intersections of the tangents form the isoptic of C.
The sinusoidal spiral is the curve for which the isoptic is also a sinusoidal spiral.

Some isoptic curves are the following:

curve isoptic
cycloid trochoid
epicycloid epitrochoid
hypocycloid hypotrochoid
parabola hyperbola

When the constant angle between the tangents has the value π/2, the curve is called an orthoptic.

For the logarithmic spiral its orthoptic is equal to itself.

Some other orthoptic curves are:

curve orthoptic
astroid quadrifolium
cardioid limašon
deltoid circle
parabola directrix

La Hire (1704) was the first to mention the curve.

Another curve with isoptic properties is the isoptic cubic.