Geography Reference
In-Depth Information
Equations for calculating a sinusoidal projection
x
=
R
λ
(cos
δ
)
y
=
R
δ
Where
φ
is the latitude and
λ
is the longitude,
R
is the radius of the earth
measured at the scale of map.
In-Depth
Calculating Projections with Radians
You may need to use radians for an exercise calculating projections or for
other angular measures. The sinusoidal projection, many other projections,
and other measures involving angles are often calculated with radians, which is
another form of angle measures: 1
∏
∏
radians.
Radians indicate the length of that part of the circle cut off by the angle, and
make it easy to determine distances on circular edges or round surfaces.
/180 radians, 360
°
=2
°
=
∏
)/180
radians = (degrees ·
The length of part of a circle (called an arc) is determined by multiplying the
number of radians by the radius. For example, the length of an arc defined by
an angle of 10
on a circle with a 100-m radius is 0.1745.
1. Determine radian measure of angle
n
radians = (10
°
°×
∏
/180)
n
radians = 0.1745
2. Calculate length of the arc
arc length =
n
radians
×
radius
arc length = 0.1745
×
100 m
arc length = 17.45
Some common angle measures in degrees and their equivalents in radians are
listed here.
Degrees
Radians
∏
/2
90
°
∏
/3
60
°
∏
/4
45
°
∏
/6
30
°
∏
/6
30
°
Lambert Projection
The cylindrical equal-area projection shown here is one of several projec-
tions that Lambert developed in the 18th century. It remains a widely used
projection, especially in atlases showing comparisons between different
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