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table of integrals | A Wisdom Archive on table of integrals |  | table of integrals A selection of articles related to table of integrals |  |
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| ARTICLES RELATED TO table of integrals |  |  |  | table of integrals: Encyclopedia II - Trigonometric function - Series definitionsPlease note: Here, and generally in calculus, all angles are measured in radians. (See also below).
Using only geometry and properties of limits, it can be shown that the derivative of sine is cosine and the derivative of cosine is the opposite of sine. One can then use the theory of Taylor series to show that the following identities hold for all real numbers x:
These identities are often taken as the definitions of the sine and cosine function. They are often used ...
See also:Trigonometric function, Trigonometric function - List of trigonometric functions, Trigonometric function - History, Trigonometric function - Right triangle definitions, Trigonometric function - Mnemonics, Trigonometric function - Slope definitions, Trigonometric function - Unit-circle definitions, Trigonometric function - Series definitions, Trigonometric function - Relationship to exponential function, Trigonometric function - Definitions via differential equations, Trigonometric function - The significance of radians, Trigonometric function - Other definitions, Trigonometric function - Computation, Trigonometric function - Inverse functions, Trigonometric function - Identities, Trigonometric function - Properties and applications, Trigonometric function - Law of sines, Trigonometric function - Law of cosines, Trigonometric function - Law of tangents Read more here: » Trigonometric function: Encyclopedia II - Trigonometric function - Series definitions |
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|  |  |  | table of integrals: Encyclopedia II - Trigonometric function - Unit-circle definitionsThe six trigonometric functions can also be defined in terms of the unit circle, the circle of radius one centered at the origin. The unit circle definition provides little in the way of practical calculation; indeed it relies on right triangles for most angles. The unit circle definition does, however, permit the definition of the trig functions for all positive and negative arguments, not just for angles between 0 and π/2 radians. It also provides a single visual picture that encapsulates at once all the important triangles used ...
See also:Trigonometric function, Trigonometric function - List of trigonometric functions, Trigonometric function - History, Trigonometric function - Right triangle definitions, Trigonometric function - Mnemonics, Trigonometric function - Slope definitions, Trigonometric function - Unit-circle definitions, Trigonometric function - Series definitions, Trigonometric function - Relationship to exponential function, Trigonometric function - Definitions via differential equations, Trigonometric function - The significance of radians, Trigonometric function - Other definitions, Trigonometric function - Computation, Trigonometric function - Inverse functions, Trigonometric function - Identities, Trigonometric function - Properties and applications, Trigonometric function - Law of sines, Trigonometric function - Law of cosines, Trigonometric function - Law of tangents Read more here: » Trigonometric function: Encyclopedia II - Trigonometric function - Unit-circle definitions |
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|  |  |  | table of integrals: Encyclopedia II - Trigonometric function - Right triangle definitionsIn order to define the trigonometric functions for the angle A, start with an arbitrary right triangle that contains the angle A:
We use the following names for the sides of the triangle:
The hypotenuse is the side opposite the right angle, or defined as the longest side of a right-angled triangle, in this case h.
The opposite side is the side opposite to the angle we are interested in, in this case a.
The adjacent side is the side that is in contact with the angle we are interested in and the right angl ...
See also:Trigonometric function, Trigonometric function - List of trigonometric functions, Trigonometric function - History, Trigonometric function - Right triangle definitions, Trigonometric function - Mnemonics, Trigonometric function - Slope definitions, Trigonometric function - Unit-circle definitions, Trigonometric function - Series definitions, Trigonometric function - Relationship to exponential function, Trigonometric function - Definitions via differential equations, Trigonometric function - The significance of radians, Trigonometric function - Other definitions, Trigonometric function - Computation, Trigonometric function - Inverse functions, Trigonometric function - Identities, Trigonometric function - Properties and applications, Trigonometric function - Law of sines, Trigonometric function - Law of cosines, Trigonometric function - Law of tangents Read more here: » Trigonometric function: Encyclopedia II - Trigonometric function - Right triangle definitions |
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| |  |  |  | table of integrals: Encyclopedia II - Trigonometric function - Other definitionsTheorem: There exists exactly one pair of real functions s, c with the following properties:
For any :
...
See also:Trigonometric function, Trigonometric function - List of trigonometric functions, Trigonometric function - History, Trigonometric function - Right triangle definitions, Trigonometric function - Mnemonics, Trigonometric function - Slope definitions, Trigonometric function - Unit-circle definitions, Trigonometric function - Series definitions, Trigonometric function - Relationship to exponential function, Trigonometric function - Definitions via differential equations, Trigonometric function - The significance of radians, Trigonometric function - Other definitions, Trigonometric function - Computation, Trigonometric function - Inverse functions, Trigonometric function - Identities, Trigonometric function - Properties and applications, Trigonometric function - Law of sines, Trigonometric function - Law of cosines, Trigonometric function - Law of tangents Read more here: » Trigonometric function: Encyclopedia II - Trigonometric function - Other definitions |
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