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HP 9g Converting Angles and Times
Angle measurements
The amount of turning between two rays with a common origin, or the measure of change of direction, is what we call am
angle. Angles cannot be meters in meters or yards. As measures of the amount of turning, we use degrees, radians and
grads.
It is important to understand that there are two ways of expressing an angle in degrees: using decimal degrees and
using degrees, minutes and seconds. In decimal degrees, an angle is simply given as 33.5 degrees, that is to say, 33
degrees and a half. In the degrees, minutes, seconds (or DMS) format, the same angle is 33 degrees, 30 minutes.
The HP 9g can work with angles in either measurement system and provides the DRG (X) and DMS (~z)
menus to convert between them. It also has the DMS function ((~z„=) which is useful when converting
between the two formats of angles in degrees.
Time measurements
As units of time, a minute is equal to 60 seconds and a second (abbreviated as s) is the fundamental unit of time in the
SI system. Since an hour has 60 minutes, a useful application of the conversion between decimal degrees and DMS
angles is that the exact same conversion can also work for time. A measurement of 10.5 hours can be converted into 10
hours and 30 minutes by the same process (i.e. using the same function,
converted into 10 degrees, 30 minutes.
Practice solving problems involving angles and times
Example 1: Convert an angle of 25 degrees into radians.
Solution:
Like many other calculators, the HP 9g operates in an angle mode that the user should specify before
doing certain calculations such as trigonometric functions and coordinate conversions. Such mode can be
selected in the DRG menu. Press X and use the „ and † keys to select the desired mode, in this case,
select RAD and press =. The angle mode annunciator is now a small R, for radians. Now , all angles will
be in radians unless stated otherwise. We need to enter 25 degrees, so we must use a way of telling the
calculator that this angle is not expressed in radians. This is done by placing the degree symbol (º) after the
quantity 25, and such symbol is in the DMS menu. Press:
25~z=
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A degree is one 360th of a complete turn and its symbol is º. Just like a meter which has
multiples and submultiples (e.g. kilometer, millimeter, etc), degrees are broken down into
minutes and seconds. The minute (') is one sixtieth of a degree, and the second ('') is one
sixtieth of a minute. The radian is defined as the angle subtended by an arc of a circle of
length equal to its radius (see figure 1). Its symbol is
Note that the counterclockwise direction of turning is taken to be positive. Grads are a
measure of angle equal to one hundredth of a right angle. Grads are also known as gradians
and grades. Angle units can be easily converted since:
π
2
=
radians
degrees
360
- 2 -
(though this symbol is not widely used).
C
=
gra
ds
400
DMS) an angle of 10.5 degrees can be
HP 9g Converting Angles and Times - Version 1.0
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