Explanation:
Trigonometry (from Greek trigōnon "triangle"
+ metron "measure"^{[1]}) is a branch of mathematics that studies triangles and the relationships between their sides and the angles between
these sides. Trigonometry defines the trigonometric
functions, which describe those relationships and have applicability to
cyclical phenomena, such as waves. It
has applications in both pure mathematics and applied
mathematics, where it is essential in many branches of science and technology.
http://en.wikipedia.org/wiki/Trigonometry
List of trigonometric
identities
In mathematics, trigonometric identities are
equalities that involve trigonometric functions and are
true for every single value of the occurring variables.
Geometrically, these are identities involving certain functions of one or more angles.
These identities are
useful whenever expressions involving trigonometric functions need to be simplified.
An important application is the integration of non-trigonometric functions: a common technique involves first
using the substitution rule with a trigonometric function, and then
simplifying the resulting integral with a trigonometric identity.
Trigonometric functions
The primary trigonometric functions are the sine and cosine of an angle. These are sometimes
abbreviated sin (θ) and cos (θ), respectively, where θ is the angle, but the parentheses
around the angle are often omitted, e.g., sin θ and cos θ.
The tangent (tan) of an angle is the ratio of the sine to the cosine:
Finally, the reciprocal
functions secant (sec), cosecant
(csc), and cotangent (cot) are the reciprocals of the cosine, sine, and
tangent:
(Our solved example in mathguru.com uses this concept).
These definitions are sometimes referred to as ratio identities.
Pythagorean
identity
The basic relationship between the sine and the cosine is the Pythagorean trigonometric identity:
(Our solved example in mathguru.com uses this concept).
where sin^{2} θ means (sin
(θ))^{2}.
This can be viewed as a version of the Pythagorean Theorem, and follows from
the equation x^{2} + y^{2} = 1 for the unit circle.
This equation can be solved for either the sine or the cosine:
http://en.wikipedia.org/wiki/Trigonometry
The
above explanation is copied from Wikipedia, the free encyclopedia and is
remixed as allowed under the Creative Commons Attribution- ShareAlike 3.0 Unported
License.