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2. Law of tangents - Wikipedia

   en.wikipedia.org/wiki/Law_of_tangents

   In trigonometry, the law of tangents or tangent rule [1] is a statement about the relationship between the tangents of two angles of a triangle and the lengths of the opposing sides.

3. Small-angle approximation - Wikipedia

   en.wikipedia.org/wiki/Small-angle_approximation

   These approximations have a wide range of uses in branches of physics and engineering, including mechanics, electromagnetism, optics, cartography, astronomy, and computer science. [ 1 ] [ 2 ] One reason for this is that they can greatly simplify differential equations that do not need to be answered with absolute precision.

4. List of trigonometric identities - Wikipedia

   en.wikipedia.org/wiki/List_of_trigonometric...

   Trigonometric functions and their reciprocals on the unit circle. All of the right-angled triangles are similar, i.e. the ratios between their corresponding sides are the same. For sin, cos and tan the unit-length radius forms the hypotenuse of the triangle that defines them.

5. Tangent half-angle formula - Wikipedia

   en.wikipedia.org/wiki/Tangent_half-angle_formula

   The sides of this rhombus have length 1. The angle between the horizontal line and the shown diagonal is ⁠ 1 / 2 ⁠ (a + b).This is a geometric way to prove the particular tangent half-angle formula that says tan ⁠ 1 / 2 ⁠ (a + b) = (sin a + sin b) / (cos a + cos b).

6. Proofs of trigonometric identities - Wikipedia

   en.wikipedia.org/wiki/Proofs_of_trigonometric...

   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 and the ratio between their sides.

7. Tangent space - Wikipedia

   en.wikipedia.org/wiki/Tangent_space

   In mathematics, the tangent space of a manifold is a generalization of tangent lines to curves in two-dimensional space and tangent planes to surfaces in three-dimensional space in higher dimensions.