Trigonometry deals with angles and their applications. The Greek mathematician Hipparchus is considered the originator of trigonometry in the 2nd century BC. He was the first to calculate trigonometric functions by inscribing triangles in circles. He created tables of values for the chord (tendon), which is twice the sine of half the angle. The names of the main trigonometric functions - sine, cosine, tangent - come from Latin and describe the lines they measure in a circle. The sine is half the tendon, the cosine refers to the complement of the angle, and the tangent touches the circle.

1. ORIGIN OF THE NAME OF
TRIGONOMETRIC FUNCTIONS
LANA ŠANIĆ, SŠ MARKANTUNA DE
DOMINISA RAB, 3.G, 20.12.2020

2. Content
• Trigonometry
• Hipparchus
• Names of trigonometric functions
•Sources

3. Trigonometry
• trigonometry is a branch of mathematics that deals with the specific functions of
angles and their application.
• the name trigonometry is a word of Greek origin, and is derived from the words
trigonon - triangle and metreo - measure.
• divided into: planar (angles and distances in the plane)
spherical (angles and distances in space).

4. Hipparchus
• The originator of trigonometry is considered to be
the Greek astronomer and mathematician Hipparchus
of Nicea (c. 180-125 BC).
• Hipparchus was the first to calculate the values of
trigonometric functions by inscribing each triangle in a
circle so that the sides of the triangle represent the
chords of the circle. To calculate the parts of a
triangle, he had to find the length of the tendon as a
function of the central angle
• In the lost work entitled Ton en kukloi eutheion (the line
inside the circle) he included in the table the values for
the tendon functions showing the length of the
tendon for each angle.

5. He did this using a circuit with a circumference of 21600 and a radius of
3438 units. These units were 1 arc minute long along the range. He made a
table with the values of the functions for angles with a difference of 7.5 °.
Each unit formed the basis of an isosceles triangle inscribed in a circle.
Since all triangles with the same angles have sides in similar proportions,
then we can use the data from the Hipparchus table to calculate the lengths
of the sides of other isosceles triangles with the same vertex angle.
The chord of an angle is equal to the double sine of half that angle, i.e.:
tendon (A) = 2 sin (A / 2).

6. Names of
trigonometric
functions

7. Formulas

8. Sinus
• Sinus - the length of a straight line drawn
from one end of a circular arc parallel to the
tangent at the other end and completed by a
radius
• It should be seen from the figure that the
“sine line” is half the length of the
Hipparchus tendon, and is based on half of
its central angle.
• The name comes from the Latin sinus- bay,
and we can see a small bay that formed
between the sine line and the arc of a circle.

9. Tangent, cosine and
cotangent
• TANGENT
• The tangent comes from the Latin tangere-touching, because it only touches the arc of the
circle.
• COSINE
• Co + sine, abbreviated from complementi sinus in Latin, which means sinus complement
• refers to the complementary angle relative to the measured angle.
• the line marked "cotangent" of the tangent is pink
• notice that the line marked "cosine" is the sine and the pink angle.
• COTANGENT
• Three of them are inverses of the other three: cotangent = 1 / tangent
• cosecant = 1 / sinus
• cosine = 1 / secant

10. Sources
•http://www.mathos.unios.hr/~mdjumic/uploads/diplomski/BOC01.pdf
•https://oikofuge.com/names-trigonometric-functions/
•https://hr.wikipedia.org/wiki/Hiparh
•https://edutorij.e-skole.hr/share/proxy/alfresco-noauth/edutorij/api/proxy-
guest/b9455aeb-16ae-4c3a-a6b1-
da720c38c54d/html/4839_Definicije_trigonometrijskih_vrijednosti_siljastog_kuta.html
•https://english.stackexchange.com/questions/40364/what-reasoning-is-behind-the-names-
of-the-trigonometric-functions-sine-secan
•https://www.quora.com/What-actually-are-sine-cosine-and-tangent

11. Thank you for attention!