TRIGONOMETRY
What is trigonometry?
Trigonometry is the study of how the
sides and angles of a triangle are related
to each other. Interestingly, the angles
are usually measured in terms of a circle
around the xand yaxes; from there, cer-
tain formulas are calculated, much as
they are in algebra, to determine all the
angles and units. Because trigonometry
is such a mix of algebra and geometry, it
is often considered “the art of doing alge-
bra over a circle.” Although “trig” (as it is
nicknamed) is a small part of geometry, it
has numerous applications in fields such
as astronomy, surveying, maritime and
aerial navigation, and engineering.How are angles measuredin trigonometry?
Angles in trigonometry are measured using a “circle” on xand yaxes—often called
circle trig definitions. The radian measure of an angle is any real number (theta; see
illustration). Take an instance in which is greater than or equal to zero ( ≥0): Pic-
ture taking a length of string and positioning one end at zero; then stretch the other
end to 1 on the xaxis, to point P(1, 0); this is also considered the radius of the circle.
Then, in a counterclockwise direction, swing the string to another position, Q (x, y).
This results in being an angle (associated with the central angle) with a vertex O or
(0, 0) and passing through points P and Q; and because the string is “1 units” in
length all the way around, the point from Q to the vertex O will also be 1. The result-
ing angle is measured in degrees—and defined as a part of the circle’s total number
of degrees (a circle has 360 degrees); it can also be translated into radians.How are degrees and radianstranslated?
When measuring the number of degrees in a circle, another unit called radians is
often used in trigonometry. It is known that a circle is 360 degrees, with 1 degree
equal to 60 minutes (60') and 1 minute equal to 60 seconds (60''); this is also called
DMS (Degree-Minute-Second) notation. One revolution around the circle also mea-
sures 2πradians. Thus, 360° 2 πradians; or 180°πradians. Simply put, to con-
vert radians to degrees, multiply by 180/π; to convert degrees to radians, multiply by
200 π/180. The following are examples of how to convert degrees and radians:
In this example of an angle measured using
trigonometry, x^2 y^2 1.