* Trigonometric functions of rational multiples of ( except when undefined ).

# REDIRECT Trigonometric functions # Sine, _cosine, _and_tangent

# REDIRECT Trigonometric functions

Trigonometric functions are important in the study of triangles and modeling periodic phenomena, among many other applications.

Trigonometric functions are commonly defined as ratios of two sides of a right triangle containing the angle, and can equivalently be defined as the lengths of various line segments from a unit circle.

Trigonometric functions have a wide range of uses including computing unknown lengths and angles in triangles ( often right triangles ).

Trigonometric functions specify the relationships among side lengths and interior angles of a right triangle.

# REDIRECT Trigonometric functions

# REDIRECT Trigonometric functions # Reciprocal functions

Trigonometric functions of angles that are rational multiples of 2π are algebraic numbers, related to roots of unity, and can be computed with a polynomial root-finding algorithm in the complex plane.

# REDIRECT Trigonometric functions # Reciprocal functions

The graphs of the sine and Trigonometric functions # cosine | cosine functions are sinusoids of different phases.

* Trigonometric functions

Trigonometric polynomials are widely used, for example in trigonometric interpolation applied to the interpolation of periodic functions.

* Trigonometric functions and their inverses

Trigonometric functions are also applied when statisticians study seasonal periodicities, which are often represented by Fourier series.

# REDIRECT Trigonometric functions

# REDIRECT Trigonometric functions

# REDIRECT Trigonometric functions

# REDIRECT Trigonometric functions

# REDIRECT Trigonometric functions

Various expansions can be used for evaluation of Trigonometric integrals, depending on the range of the argument.

** Great Trigonometric Survey of India officially gives ' Peak XV ' ( later to be named Mount Everest ) the height of.

In South America Bouguer noticed, as did George Everest in the 19th century Great Trigonometric Survey of India, that the astronomical vertical tended to be pulled in the direction of large mountain ranges, due to the gravitational attraction of these huge piles of rock.

To complete the proof, the identities found at Trigonometric symmetry, shifts, and periodicity may be employed.

The subject of his doctoral thesis was Topics in the Theory of Uniqueness of Trigonometric Series.

The General Catalogue of Trigonometric Parallaxes, first published in 1952 and later superseded by the New GCTP ( now in its fourth edition ), covers nearly 9, 000 stars.

( Top ): Trigonometric function sinθ for selected angles θ, π − θ, π + θ, and 2π − θ in the four quadrants.

* April 10 – Great Trigonometric Survey of India begins with the measurement of a baseline near Madras.

Sir George was largely responsible for completing the section of the Great Trigonometric Survey of India along the meridian arc from the south of India extending north to Nepal, a distance of approximately.

The Great Trigonometric Survey of India, started by the East India Company in 1802, then taken over by the British Raj after 1857 was notable as a successful effort on a larger scale and for accurately determining heights of Himalayan peaks from viewpoints over one hundred miles distant.

In particular, Kater's pendulums were used in the Great Trigonometric Survey of India.

The Principal Triangulation of Great Britain was begun by the Ordnance Survey in 1783, though not completed until 1853 ; and the Great Trigonometric Survey of India, which ultimately named and mapped Mount Everest and the other Himalayan peaks, was begun in 1801.

He entered the army, obtaining a commission in the 12th Regiment of Foot, then stationed in India, where he assisted William Lambton in the Great Trigonometric Survey.

* Edmund Landau: The Master Rigorist by Eli Maor, Trigonometric Delights, page 192.

Montgomerie in 1856 when he first spotted the peaks of the Karakoram from more than 200 km away during the Great Trigonometric Survey of India.

He wrote a standard two-volume work Trigonometric Series.

* April 10-Great Trigonometric Survey of India begins with the measurement of a baseline near Madras.

* Thomas Montgomerie of the Great Trigonometric Survey of India makes the first survey of the Karakoram Range, from Mount Haramukh, to the south, and designates the two most prominent peaks as K1 and K2.

She was the author of the Bright Star Catalogue, a compendium of information on the 9, 110 brightest stars in the sky ; she also co-authored The General Catalogue of Trigonometric Stellar Parallaxes, containing precise distance measurements to 8, 112 stars, information critical to understanding the kinematics of the Milky Way galaxy and the evolution of the solar neighborhood.

Near Q, both curves can be represented by analytic functions of U.

It also has a pair of short tentacles near the eye that can be extended and which have tactile and olfactory functions.

Suanpans can be used for functions other than counting.

It can be applied in the study of classical concepts of mathematics, such as real numbers, complex variables, trigonometric functions, and algorithms, or of non-classical concepts like constructivism, harmonics, infinity, and vectors.

There are typically three mathematical forms for the radial functions R ( r ) which can be chosen as a starting point for the calculation of the properties of atoms and molecules with many electrons.

They can be obtained analytically, meaning that the resulting orbitals are products of a polynomial series, and exponential and trigonometric functions.

As they do not receive Holy Orders in the Catholic, Orthodox and Oriental Churches, they do not possess the ability to ordain any religious to Holy Orders, or even admit their members to the non-ordained ministries to which they can be installed by the ordained clergy ( females do not serve as clergy anyway, per formal church teaching, in these churches ), nor do they exercise the authority they do possess under canon law over any territories outside of their monastery and its territory ( though non-cloistered, non-contemplative female religious members who are based in a convent or monastery but who participate in external affairs may assist as needed by the diocesan bishop and local secular clergy and laity, in certain pastoral ministries and administrative and non-administrative functions not requiring ordained ministry or status as a male cleric in those churches or programs ).

As ' functions ' these can take only the value 0, but they carry infinitesimal information, in purely algebraic settings.

People can appreciate a Renaissance Madonna for aesthetic reasons, but such objects often had ( and sometimes still have ) specific devotional functions.

Organisationally and spatially these functions can be arranged in many ways.

Asymptotes of many elementary functions can be found without the explicit use of limits ( although the derivations of such methods typically use limits ).

Once logged in, a user can perform functions such as uploading and downloading software and data, reading news and bulletins, and exchanging messages with other users, either through email, public message boards, and sometimes via direct chatting.

Thus, a single " rule ," like mapping every real number x to x < sup > 2 </ sup >, can lead to distinct functions and, depending on whether the images under that rule are understood to be reals or, more restrictively, non-negative reals.

In turn, one can also derive ordinary functions of one variable from a binary function.

The various concepts relating to functions can also be generalised to binary functions.

One can also consider partial binary functions, which may be defined only for certain values of the inputs.

Physical effects of battle can include scars, amputations, lesions, loss of bodily functions, blindness, paralysis — and death.

A comparison of genes within a species or between different species can show similarities between protein functions, or relations between species ( the use of molecular systematics to construct phylogenetic trees ).

The definition works without any changes if instead of vector spaces over a field F, we use modules over a commutative ring R. It also can be easily generalized to n-ary functions, where the proper term is multilinear.

* Wave functions and other quantum states can be represented as vectors in a complex Hilbert space.

The Bessel functions can be expressed in terms of the generalized hypergeometric series as

The Bessel function of the second kind then can be thought to naturally appear as the imaginary part of the Hankel functions.

) In this way, for example, one can compute Bessel functions of higher orders ( or higher derivatives ) given the values at lower orders ( or lower derivatives ).

This orthogonality relation can then be used to extract the coefficients in the Fourier – Bessel series, where a function is expanded in the basis of the functions J < sub > α </ sub >( x u < sub > α, m </ sub >) for fixed α and varying m.