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Resource: calculus by James Stewart 8th edition
In mathematics, trigonometric identities are equalities that involve trigonometric functions and are true for every value of the occurring variables for which both sides of the equality are defined. Geometrically, these are identities involving certain functions of one or more angles. They are distinct from triangle identities, which are identities potentially involving angles but also involving side lengths or other lengths of a triangle.
These identities are useful whenever expressions involving trigonometric functions need to be simplified. An important application is the integration of nontrigonometric functions: a common technique involves first using the substitution rule with a trigonometric function, and then simplifying the resulting integral with a trigonometric identity.
Even and odd functions have properties that can be useful in different contexts. The most basic one is that for an even function if you know f(x), you know f(x). Similarly for odd functions, if you know g(x), you know g(x). Put more plainly, the functions have a symmetry that allows you to find any negative value if you know the positive value or vice versa.
The graph of a function f is the set of all points in the plane of the form (x, f(x)). We could also define the graph of f to be the graph of the equation y = f(x). So, the graph of a function if a special case of the graph of an equation.
In mathematics, even functions and odd functions are functions that satisfy particular symmetry relations, with respect to taking additive inverses. They are important in many areas of mathematical analysis, especially the theory of power series and Fourier series.
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