In Indian astronomy, the study of trigonometric functions flourished in the Gupta period, especially due to Aryabhata (sixth century CE), who discovered the sine function.
In the 12th century, Bhaskara II discovered the sine and cosine expansions in roughly their modern form. Arabic mathematicians were also working in this area and, in the 9th century, Muhammad ibn Musa al-Khwarizmi produced sine and cosine tables. He also gave a table of tangents.
In trigonometry, the name “sine” comes through Latin from a Sanskrit word meaning “chord”. In the picture of a unit circle below, AB has length sinθ and this is half a chord of the circle. The co-functions are functions of complementary angles: cosθ = sin(π/2 − θ), cotθ = tan(π/2 − θ), and cscθ = sec(π/2 − θ).
Sine was introduced by Abu'l Wafa in 8th century, as a more convenient function, and gradually spread first in the Muslim world, and then to the West. (But apparently it was used in India centuries before him), as a more convenient function. However this new notation was adopted very slowly, it took centuries.
In the twelfth century, when an Arabic trigonometry work was translated into Latin, the translator used the equivalent Latin word sinus, which also meant bosom, and by extension, fold (as in a toga over a breast), or a bay or gulf. This Latin word has now become our English “sine.”
Sin, cos, and tan are trigonometric ratios that relate the angles and sides of right triangles. Sin is the ratio of the opposite side to the hypotenuse, cos is the ratio of the adjacent side to the hypotenuse, and tan is the ratio of the opposite side to the adjacent side.
Sine is "opposite over hypotenuse" (the SOH of SOHCAHTOA). When we draw the triangle inside a unit circle the hypotenuse is automatically 1 at any angle. That means the sine of an angle is simply the length of the "opposite" leg of the triangle (opposite / 1).
The belief began to emerge in the 3rd century, but only became fully formed with the writings of Augustine of Hippo (354–430 AD), who was the first author to use the phrase "original sin" (Latin: peccatum originale).
Traditionally, the origin has been ascribed to the sin of the first man, Adam, who disobeyed God in eating the forbidden fruit (of knowledge of good and evil) and, in consequence, transmitted his sin and guilt by heredity to his descendants.
As we know, the sine function is defined for all real numbers, so the domain of y = sin x is the set of all real numbers, i.e. R. The range of sine function is the closed interval [-1, 1]. That means, -1 ≤ y ≤ 1 or -1 ≤ sin x ≤ 1.
2, page 618), "the first writer to use the symbol sin for sine in a book seems to have been the French mathematician Hérigone (1634)." However, the use by Oughtred would seem to predate that of Hérigone. Cosine. In his Geometria rotundi (1588) Thomas Fincke used sin. com. for the cosine.
Robert Recorde, the designer of the equals sign, introduced plus and minus to Britain in 1557 in The Whetstone of Witte: "There be other 2 signes in often use of which the first is made thus + and betokeneth more: the other is thus made − and betokeneth lesse."
The first recorded algorithm for rigorously calculating the value of π was a geometrical approach using polygons, devised around 250 BC by the Greek mathematician Archimedes. This polygonal algorithm dominated for over 1,000 years, and as a result π is sometimes referred to as Archimedes's constant.
Suggestions for the location of the Garden of Eden include the head of the Persian Gulf, as argued by Juris Zarins, in southern Mesopotamia where the Tigris and Euphrates rivers run into the sea; and in the Armenian Highlands or Armenian National Plateau.
There are three sins that lie behind discontent—pride, rebellion and unbelief. These are the original sins of the devil and his angels. They are sins that come from hell itself, and they continue in hell forever.
By having Mary free of original sin resulted in both Mary's and Jesus' conceptions being miraculous.
The concept of Original Sin is not part of Islamic doctrine. Muslims believe humans are born without sin and with a desire to please God. We have free will, which causes us to go astray at times, but God is always willing to forgive.
Eve picked the forbidden fruit and ate it. Adam was with her and he ate it, too. Their eyes were opened and their innocence, lost. They ran from God and His presence soon after, and were expelled from the garden, paradise also lost.
The Doctrine of Original Sin is primarily associated with the Christian, Catholic, and Protestant churches. Other religious sects, such as the Eastern Orthodox Church, did not adopt the doctrine. The idea that man is born with a sinful nature has fallen out of favor since the European Enlightenment.
The sine function oscillates from -1 to 1. Because of this the limit does not converge on a single value. which means the limit Does Not Exist.
Sine is an odd function, and cosine is an even function. You may not have come across these adjectives “odd” and “even” when applied to functions, but it's important to know them. A function f is said to be an odd function if for any number x, f(–x) = –f(x).
A sine wave or sinusoidal wave is the most natural representation of how many things in nature change state. A sine wave shows how the amplitude of a variable changes with time.
The key points for sine are (0, 0), (π2,1), (π, 0), (3π2,−1), and (2π, 0). Graph the key points and sketch the sine curve through the points. Then continue the pattern both positive and negative. The key points for cosine are (0, 1), (π2,0), (π, −1), (3π2,0), and (2π, 1).
Arcsine is the inverse of sine function. It is used to evaluate the angle whose sine value is equal to the ratio of its opposite side and hypotenuse. Therefore, if we know the length of opposite side and hypotenuse, then we can find the measure of angle.
The exact shape of a sine wave is very important to the field of electronics because it is the only wave shape that has energy at only one frequency. All other possible wave shapes contain energy at more than one frequency at the same time.