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  2. Law of cosines - Wikipedia

    en.wikipedia.org/wiki/Law_of_cosines

    The law of cosines generalizes the Pythagorean theorem, which holds only for right triangles: if is a right angle then ⁡ =, and the law of cosines reduces to = +. The law of cosines is useful for solving a triangle when all three sides or two sides and their included angle are given.

  3. List of trigonometric identities - Wikipedia

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

    Ptolemy's theorem states that the sum of the products of the lengths of opposite sides is equal to the product of the lengths of the diagonals. When those side-lengths are expressed in terms of the sin and cos values shown in the figure above, this yields the angle sum trigonometric identity for sine: sin(α + β) = sin α cos β + cos α sin β.

  4. Trigonometric functions - Wikipedia

    en.wikipedia.org/wiki/Trigonometric_functions

    The law of cosines (also known as the cosine formula or cosine rule) is an extension of the Pythagorean theorem: = + ⁡, or equivalently, ⁡ = +. In this formula the angle at C is opposite to the side c .

  5. Trigonometry - Wikipedia

    en.wikipedia.org/wiki/Trigonometry

    The law of tangents, developed by François Viète, is an alternative to the Law of Cosines when solving for the unknown edges of a triangle, providing simpler computations when using trigonometric tables. [86]

  6. Sine and cosine - Wikipedia

    en.wikipedia.org/wiki/Sine_and_cosine

    In mathematics, sine and cosine are trigonometric functions of an angle.The sine and cosine of an acute angle are defined in the context of a right triangle: for the specified angle, its sine is the ratio of the length of the side that is opposite that angle to the length of the longest side of the triangle (the hypotenuse), and the cosine is the ratio of the length of the adjacent leg to that ...

  7. Spherical law of cosines - Wikipedia

    en.wikipedia.org/wiki/Spherical_law_of_cosines

    If the law of cosines is used to solve for c, the necessity of inverting the cosine magnifies rounding errors when c is small. In this case, the alternative formulation of the law of haversines is preferable. [3] A variation on the law of cosines, the second spherical law of cosines, [4] (also called the cosine rule for angles [1]) states:

  8. Proofs of trigonometric identities - Wikipedia

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

    For example, the sine of angle θ is defined as being the length of the opposite side divided by the length of the hypotenuse. The six trigonometric functions are defined for every real number , except, for some of them, for angles that differ from 0 by a multiple of the right angle (90°).

  9. Pythagorean trigonometric identity - Wikipedia

    en.wikipedia.org/wiki/Pythagorean_trigonometric...

    Similar right triangles illustrating the tangent and secant trigonometric functions Trigonometric functions and their reciprocals on the unit circle. The Pythagorean theorem applied to the blue triangle shows the identity 1 + cot 2 θ = csc 2 θ, and applied to the red triangle shows that 1 + tan 2 θ = sec 2 θ.