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Trigonometric functions specify the relationships among side lengths and interior angles of a right triangle.
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Trigonometric and functions
* Trigonometric functions of rational multiples of ( except when undefined ).
# REDIRECT Trigonometric functions # Sine, _cosine, _and_tangent
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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 ).
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# REDIRECT Trigonometric functions # Reciprocal functions
Trigonometric functions can be expressed in terms of complex exponentiation.
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
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Trigonometric and angles
( Top ): Trigonometric function sinθ for selected angles θ, π − θ, π + θ, and 2π − θ in the four quadrants.
* Trigonometric basis for increased wheel strength at reduced spoke angles ( Archived 2009-10-22 )
Trigonometric and .
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The General Catalogue of Trigonometric Parallaxes, first published in 1952 and later superseded by the New GCTP ( now in its fourth edition ), covers nearly 9, 000 stars.
* April 10 – Great Trigonometric Survey of India begins with the measurement of a baseline near Madras.
** Great Trigonometric Survey of India officially gives ' Peak XV ' ( later to be named Mount Everest ) the height of.
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.
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.
Various expansions can be used for evaluation of Trigonometric integrals, depending on the range of the argument.
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.
functions and specify
Cumulative distribution functions are also used to specify the distribution of multivariate random variables.
The Kolmogorov extension proceeds along the following lines: assuming that a probability measure on the space of all functions exists, then it can be used to specify the joint probability distribution of finite-dimensional random variables.
When dealing with functions of multiple variables, some of these variables may be related to each other, and it may be necessary to specify explicitly which variables are being held constant.
* Security Functional Requirements ( SFRs ) – specify individual security functions which may be provided by a product.
where the functions q and p take values in a vector space, and function is the ( scalar valued ) Hamiltonian function, and specify the domain of values in which the parameter t ( time ) varies.
The conventional Van der Waals equation is a mechanical equation of state, which cannot be used to specify all thermodynamic functions, while the statistical mechanical derivation yields the partition function for the system, which does allow all thermodynamic functions to be specified, including the mechanical equation of state.
Shh functions in a concentration-dependent manner to specify ventral neuronal fates.
With time, like many titles, the term was applied to more and varied functions, leading to compound titles to specify various secretarial work better, like general secretary or financial secretary.
Because Fieldata did not specify codes for interconnection and data transmission control, different systems used different control functions.
Ad-hoc polymorphism is a dispatch mechanism: control moving through one named function is dispatched to various other functions without having to specify the exact function being called.
Most economists specify social welfare functions that are intermediate between these two extremes.
Its fifteen sections establish certain civil service offices, specify their functions and jurisdictions, set out the qualifications and preconditions required of persons holding such offices, and prescribes the manner of their appointment.
Sections 147 through 151 specify the functions of the Public Service Commission.
Sections 152 through 154 specify the functions of Disciplined Services Commission.
* Generic typeclasses, which specify functions solely in terms the algebraic structure of the types they operate on.
PHP 5. 3's anonymous functions allow one to specify variables to include in the closure using the clause ; if the variable is listed by reference, it includes a reference to the original variable ; otherwise, it makes a copy.
# Interfaces are bidirectional: they specify a set of functions to be implemented by the interface's provider ( commands ) and a set to be implemented by the interface's user ( events ).
For each value of τ and σ, these functions specify a unique spacetime vector:
The current Official Languages Act was adopted in 1988 to improve the 1969 law's efforts to address two basic policy objectives: ( 1 ) to specify the powers, duties and functions of federal institutions relevant to official languages ; ( 2 ) to support the development of linguistic minority communities.
These functions specify initial data, from which a unique vacuum solution can be evolved.
In a Bayesian game, it is necessary to specify the strategy spaces, type spaces, payoff functions and beliefs for every player.
You can also specify a timeout on the wait using the or member functions to avoid indefinite blocking.
Notice that while in general it requires ten functions to specify a fluid, a perfect fluid requires only two, and dusts and radiation fluids each require only one function.
1.383 seconds.