# Sinusoidal

## Description

The sinusoidal projection is a pseudocylindrical equal-area projection displaying all parallels and the central meridian at true scale. The boundary meridians bulge outward excessively producing considerable shape distortion near the map outline. Alternative formats reduce the distortion along outer meridians by interrupting the continuity of the projection over the oceans and by centering the continents around their own central meridians, or vice versa.

The sinusoidal projection is also known as the Sanson-Flamsteed and Mercator-Sanson projection after the cartographers who used it. The projection was developed in the 16th century. It is available in ArcGIS Pro 1.0 and later and in ArcGIS Desktop 8.0 and later.

## Projection properties

The subsections below describe the sinusoidal projection properties.

### Graticule

Sinusoidal is a pseudocylindric projection. The equator and the central meridian are projected as straight lines, where the projected equator is two times as long as the central meridian. The other meridians are sinusoidal curves, bulging away from the central meridian and equally spaced. The parallels are equally spaced straight lines perpendicular to the central meridian. The poles are presented as points and they appear as protruding edges. The graticule is symmetric across the equator and the central meridian.

### Distortion

Sinusoidal is an equal-area (equivalent) projection. Shapes, directions, angles, and distances are generally distorted. Scale is true along every parallel and the central meridian. Distortions are moderate near the projection center. Bulging meridians produce considerable distortion toward the edge of the projection. Distortion values are symmetric across the equator and the central meridian.

## Usage

The sinusoidal projection is appropriate for thematic world maps although its use is not recommended. The projection has also been used for maps of continents near the equator, like South America and Africa, centered on their own central meridians.

## Parameters

Sinusoidal parameters are as follows:

• False Easting
• False Northing
• Central Meridian

## Sources

Snyder, J. P. (1987). Map Projections: A Working Manual. U.S. Geological Survey Professional Paper 1395. Washington, DC: United States Government Printing Office.

Snyder, J. P. (1993). Flattening the Earth. Two Thousand Years of Map Projections. Chicago and London: University of Chicago Press.

Snyder, J. P. and Voxland, P. M. (1989). An Album of Map Projections. U.S. Geological Survey Professional Paper 1453. Washington, DC: United States Government Printing Office.