Collection of proofs of equations involving trigonometric functions
There are several equivalent ways for defining trigonometric functions, and the proofs of the trigonometric identities between them depend on the chosen definition. The oldest and most elementary definitions are based on the geometry of right triangles. The proofs given in this article use these definitions, and thus apply to non-negative angles not greater than a right angle. For greater and negative angles, see Trigonometric functions.
Other definitions, and therefore other proofs are based on the Taylor series of sine and cosine, or on the differential equation to which they are solutions.
and 23 Related for: Proofs of trigonometric identities information
are several equivalent ways for defining trigonometric functions, and the proofsof the trigonometricidentities between them depend on the chosen definition...
In trigonometry, trigonometricidentities are equalities that involve trigonometric functions and are true for every value of the occurring variables for...
not in the interval [0, π/2], see Proofsoftrigonometricidentities). For non-geometrical proofs using only tools of calculus, one may use directly the...
Pythagorean trigonometricidentity, also called simply the Pythagorean identity, is an identity expressing the Pythagorean theorem in terms oftrigonometric functions...
sine theorem Polar sine—a generalization to vertex angles Proofsoftrigonometricidentities Sinc function Sine and cosine transforms Sine integral Sine...
a trigonometric way) that are equivalent to specific trigonometric laws or formulas. For instance, propositions twelve and thirteen of book two of the...
functions, and are used to obtain an angle from any of the angle's trigonometric ratios. Inverse trigonometric functions are widely used in engineering, navigation...
traditionally expressed using trigonometric functions. On the sphere, geodesics are great circles. Spherical trigonometry is of great importance for calculations...
earliest-known tables of values for trigonometric ratios (also called trigonometric functions) such as sine. Throughout history, trigonometry has been applied...
mathematical identities are relatively simple (for an experienced mathematician), though not necessarily unimportant. Trivial logarithmic identities are: By...
mathematical theorem. The proofs are diverse, including both geometric proofs and algebraic proofs, with some dating back thousands of years. When Euclidean...
Divergence Theorem . Half-side formula Law of sines Law of tangents Law of cotangents List oftrigonometricidentities Mollweide's formula Given sides b , c...
divisors Table of integrals Table of mathematical symbols Table of prime factors Taylor series Timeline of mathematics Trigonometricidentities Truth table...
differentiation oftrigonometric functions is the mathematical process of finding the derivative of a trigonometric function, or its rate of change with respect...
exercised with trigonometric functions and trigonometricidentities. The binomial theorem, polar coordinates, parametric equations, and the limits of sequences...
logarithms that would supplant it. The trigonometricidentities exploited by prosthaphaeresis relate products oftrigonometric functions to sums. They include...
As an alternative to using the identity for the sum or difference of two sines, one may cite the trigonometricidentity tan 1 2 ( α ± β ) = sin α ±...
correspond to a log-n-step loop. Because of that, proofs using prefix induction are "more feasibly constructive" than proofs using predecessor induction. Predecessor...
)&=&2a(1-\cos \varphi )\cdot \sin \varphi &.&\end{array}}} (The trigonometricidentities e i φ = cos φ + i sin φ , ( cos φ ) 2 + ( sin φ ) 2 =...
of a periodic function into a sum oftrigonometric functions. The Fourier series is an example of a trigonometric series, but not all trigonometric series...
law of sines is one of two trigonometric equations commonly applied to find lengths and angles in scalene triangles, with the other being the law of cosines...
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