Who invented trigonometric functions

As I said for formal you need real analysis and mathematical experience. Did they know and use it? Did they even use radians? I know how to formally prove it, that's not what I'm asking. I'm asking how it was originally discovered.

And this specific fact was known to Manjula around and Aryabhata II around and explicitly given with geometric reasoning by Bhaskara II around even before the general calculus or power series of Madhava around Show 4 more comments.

Active Oldest Votes. Improve this answer. KCd KCd 3, 11 11 silver badges 21 21 bronze badges. Add a comment. ShreevatsaR ShreevatsaR 5 5 silver badges 6 6 bronze badges. It will take me a bit of effort to go through the French, but it is not surprising that this sort of geometric reasoning for trigonometry predates even by centuries a general calculus of arbitrary functions. Alexei Kopylov Alexei Kopylov 2 2 silver badges 6 6 bronze badges.

See my answer. But Sin x has been used historically to calculate pi thus making the definitions of Sin x and pi circular. Is that right? Sign up or log in Sign up using Google. Sign up using Facebook. Its applications include in:. Trigonometry has many real-life examples used broadly. A boy is standing near a tree. What we have here is a right-angled triangle, i. Trigonometric formulas can be applied to calculate the height of the tree, if the distance between the tree and boy, and the angle formed when the tree is viewed from the ground is given.

It is determined using the tangent function, such as tan of angle is equal to the ratio of the height of the tree and the distance. Example 1: The building is at a distance of feet from point A. The base and height of the building form a right-angle triangle. Example 2: A man observed a pole of height 60 ft.

According to his measurement, the pole cast a 20 ft long shadow. Find the angle of elevation of the sun from the tip of the shadow using trigonometry. Trigonometry is the branch of mathematics that deals with the study of the relationship between the sides of a triangle right-angled triangle and its angles. The relationship is presented as the ratio of the sides, which are trigonometric ratios.

The six trigonometric ratios are sine, cosine, tangent, cotangent, secant, and cosecant. There are six basic trigonometric ratios: sine, cosine, tangent, cosecant, secant and cotangent. All the important concepts covered under trigonometry are based on these trigonometric ratios or functions. Trigonometry finds applications in different fields in our day-to-day lives. In astronomy, trigonometry helps in determining the distances of the Earth from the planets and stars.

It is used in constructing maps in geography and navigation. It can also be used in finding an island's position in relation to the longitudes and latitudes. Even today, some of the technologically advanced methods which are used in engineering and physical sciences are based on the concepts of trigonometry. It is the angle between the horizontal plane and the line of sight from an observer's eye to an object above.

Trigonometry identities are equations of trigonometry functions that are always true. Trigonometry identities are often used not only to solve trigonometry problems but also to understand important mathematical principles and solve numerous math problems. The reciprocal of sin function is given as cosecant function. Trigonometry in real life is used in the naval and aviation industries. It also finds application in cartography creation of maps. It can be used to design the inclination of the roof and the height of the roof in buildings etc.

It's easy forget that the people who defined them were not sadistic math teachers who want people to memorize weird functions for no reason. These functions actually made computations quicker and less error-prone. Now that computers are so powerful, the haversine has gone the way of the floppy disc. But I think we can all agree that it should come back, if only for the "awesome" joke I came up with as I was falling asleep last night: Haversine?

I don't even know 'er! You've been warned. In the table of secret trig functions, "ha" clearly means half; the value of haversine is half of the value of versine, for example.

Complementary angles add up to 90 degrees. In a right triangle, the two non-right angles are complementary. For instance, the cosine of an angle is also the sine of the complementary angle. Likewise, the coversine is the versine of the complementary angle, as you can see in light blue above one of the red sines in the diagram at the top of the post. The one bonus trig function that confuses me a little bit is the vercosine. If the "co" in that definition meant the complementary angle, then vercosine would be the same as coversine, which it isn't.

Instead, the vercosine is the versine of the supplementary angle supplementary angles add up to degrees , not the complementary one. My guess is that vercosine was a later term, an analogy of the square of sine definition of versine using cosine instead.

If you're a trigonometry history buff and you have more information, please let me know! In any case, the table of super-secret bonus trig functions is a fun exercise in figuring out what prefixes mean. The views expressed are those of the author s and are not necessarily those of Scientific American. Follow Evelyn Lamb on Twitter. Already a subscriber? Sign in. Thanks for reading Scientific American. Create your free account or Sign in to continue. See Subscription Options.

Go Paperless with Digital. It's well known that you can shake a stick at a maximum of 8 trig functions. The familiar sine, cosine, and tangent are in red, blue, and, well, tan, respectively.