Sinusoidal projection

[1] The projection represents the poles as points, as they are on the sphere, but the meridians and continents are distorted.

Therefore, the length of each parallel on the map is proportional to the cosine of the latitude, as it is on the globe.

This makes the left and right bounding meridians of the map into half of a sine wave, each mirroring the other.

Each meridian is half of a sine wave with only the amplitude differing, giving the projection its name.

The MODLAND Integerized Sinusoidal Grid, based on the sinusoidal projection, is a geodesic grid developed by the NASA's Moderate-Resolution Imaging Spectroradiometer (MODIS) science team.

Sinusoidal projection of the world.
The sinusoidal projection with Tissot's indicatrix of deformation
Jean Cossin, Carte cosmographique ou Universelle description du monde, Dieppe, 1570
A sinusoidal projection shows relative sizes accurately, but distorts shapes and directions. Distortion can be reduced by "interrupting" the map.