Game Development Reference
In-Depth Information
The measure of an angle
has no maximum value in degrees. If it extends
upward from the origin, following the path of the
y
axis of the Cartesian plane, its
measure is 90
. Since the line is perpendicular to the initial side, you call it a right
angle. If the line extends to the left of the origin, its measure is 180
8
8
, and you call
it a straight angle. An angle of 270
follows the
y
axis downward and is also
perpendicular to the initial side. You can call it a right angle, also.
8
If an angle measures 450
8
, it is the same as one revolution of the circle plus 90
8
,so
it is a right angle. If an angle measures 540
8
, it is the same as one revolution of the
8
circle plus 180
, and it is a straight angle. In this respect, if someone tells you to
turn a screw 1440
degrees to the right, then, you determine the number of terms
by dividing the degrees by the circumference of a circle:
1440
8
8
8
¼
4. The measure of
the angle from the initial size to the terminal side is 0. No remainder is left after
the division.
360
Circumference and Radians
The radius of a circle consists of a line extending from the center of the circle to
any point on its perimeter. The circumference of a circle is a measure of the arc of
a complete circle. To calculate the circumference of a circle, you multiply 2 times
by the radius of the circle. Here is the equation:
C
¼
2
r
The variable C signifies the circle's circumference, while
r
represents the radius,
and
is an irrational number with an approximate value of 3.14. Given this
representation of a circle, you can describe a circle in terms of radians.
A radian is an arc on the perimeter of a circle that is equal in length to the radius
of the circle. Given the equation C
¼
2
radians in a
complete circle. In other words, if you travel around the circle a distance equal
in length to the radius multiplied by 2
r
, then, there are 2
,youendupwhereyoustarted.
A radian is an arc equal
in length to the radius of a circle. If you use
an approximate value for
of 3.14 and multiply by 2, then you can say
that 6.28 radians can be placed head to tail to complete one revolution of a
circle.
As Figure 12.7 illustrates, you can relate the size of an angle using radians. The
procedure involves using
part of a quotient. To accomplish
this task, consider how to designate the four directions of the compass using
alone or making
