Exercise Steps and Questions
In this exercise you will be calculating a projection of a graticule. You will have to do
the calculations and show that you have done them, but you can work with other
people to check your answers and determine the process. Before the calculating
part of this exercise, let's look at the fundamental problems of projecting a spherical
object on a plane.
In Part 2 of this exercise, you will need to make the calculations in radians. Radians
are one of three ways to measure angles. They are mainly used for engineering and
science. We won't spend much time getting into the mathematics of angular mea-
sures. For this exercise, you only need to understand the relationship between
degree and radian measures of angles.
If you know an angle measure in degrees, you can easily convert it to radians,
another measure for angles used in engineering and scientific calculations:
radians = (degrees · ?)/180
For example, 180 degrees equals 3.14 radians; 90 degrees equals 1.57 radians; 45
degrees equals 0.785 radians. As the examples show, radians express angular mea-
sures in relationship to the radius.
STEP 1: CALCULATE THE PROJECTION
Use the table below for recording the results of your calculations. The rows indicat-
ing latitude are on the left and the columns indicating longitude are on the top. You
will be calculating the sinusoidal projection for latitudes 0 ° ,30 ° ,60 ° , and 90 ° , and for
longitudes 0 ° ,30 ° ,60 ° ,90 ° , 120 ° , 150 ° , and 180 ° . Your results will be in kilometers,
or, for an idealized projection surface, about 10,000 km in length and height.
The equations you will use are:
x = radius · longitude · cosine (latitude)
y = radius · latitude
Where: radius = 6,371 km.
Remember: convert all angle measures from degrees to radians by multiplying by pi
and dividing by 180 degrees. For example, 30 ° corresponds to pi/6 using this equa-
radians = (degrees ·
Table of projected values (Step 1)