Table of Contents
How did trig functions get their name?
In trigonometry, the name “sine” comes through Latin from a Sanskrit word meaning “chord”. The names “tangent” and “secant” come from lengths of line segments that are either tangent to the unit circle or cut through a unit circle; a line that cuts through a circle is called a secant line.
Why are sin cos and tan named as they are?
The meanings of these words are very similar: the sine of an angle in a right triangle is the ratio of the opposite side to the hypotenuse; the secant is the ratio of the hypotenuse to the adjacent side, and the tangent is the ratio of the opposite side to the adjacent side.
How trigonometric functions are defined?
Definition of trigonometric function 1 : a function (such as the sine, cosine, tangent, cotangent, secant, or cosecant) of an arc or angle most simply expressed in terms of the ratios of pairs of sides of a right-angled triangle.
Where does the name cosine come from?
The word “sine” (Latin “sinus”) comes from a Latin mistranslation by Robert of Chester of the Arabic jiba, which is a transliteration of the Sanskrit word for half the chord, jya-ardha. The word “cosine” derives from a contraction of the Medieval Latin “complementi sinus”.
Why is Tan called tangent?
In geometry, the tangent line (or simply tangent) to a plane curve at a given point is the straight line that “just touches” the curve at that point. Leibniz defined it as the line through a pair of infinitely close points on the curve. The word “tangent” comes from the Latin tangere, “to touch”.
Are all trigonometric functions periodic?
1: All trigonometric functions are periodic on “R”. The functions sinx,cosx,secxandcosecx have periodicity of “2π”.
Who invented trigonometry?
Hipparchus
Trigonometry in the modern sense began with the Greeks. Hipparchus (c. 190–120 bce) was the first to construct a table of values for a trigonometric function.
Who is Sohcahtoa?
SOHCAHTOA is a mnemonic device used to remember the ratios of sine, cosine, and tangent in trigonometry.
What is a trigonometric function?
It wasn’t until the 16th century that Georg Joachim Rhaeticus, a Teutonic astronomer, defined the trigonometric functions as the ratios of the sides of a right triangle as we use them today. In the diagram below, using a standard rectangular coordinate system, you see a unit circle of radius 1 with its center at the origin (0, 0).
How are the six trigonometric values of a circle defined?
Introduction: Originally, all six trigonometric values were defined by the lengths of the sides of the triangles, the chord, and the secant as shown in the following unit circle diagram.
What is the trigonometric ratio table for six functions?
The trigonometric ratio table for six functions like Sin, Cos, Tan, Cosec, Sec, Cot, are: Trigonometric Ratios/ angle= θ in degree 0 ° 30 ° 45 ° 90 ° Sin θ 0 1/2 1/√2 1 Cos θ 1 √3/2 1/√2 0 Tan θ 0 1/√3 1 ∞ Cosec θ ∞ 2 √2 1
What is the difference between trigonometry functions and Pythagorean identities?
The trig functions are the periodic functions. The smallest periodic cycle is 2π but for tangent and the cotangent it is π. Where n is any integer. When the Pythagoras theorem is expressed in the form of trigonometry functions, it is said to be Pythagorean identity. There are majorly three identities: