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  2. List of trigonometric identities - Wikipedia

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

    The half-angle formula for cosine can be obtained by replacing with / and taking the square-root of both sides: ⁡ (/) = (+ ⁡) /. Sine power-reduction formula: an illustrative diagram. The shaded blue and green triangles, and the red-outlined triangle E B D {\displaystyle EBD} are all right-angled and similar, and all contain the angle θ ...

  3. Inverse trigonometric functions - Wikipedia

    en.wikipedia.org/wiki/Inverse_trigonometric...

    Specifically, they are the inverses of the sine, cosine, tangent, cotangent, secant, and cosecant functions, [4] and are used to obtain an angle from any of the angle's trigonometric ratios. Inverse trigonometric functions are widely used in engineering, navigation, physics, and geometry.

  4. Trigonometric functions - Wikipedia

    en.wikipedia.org/wiki/Trigonometric_functions

    Circa 830, Habash al-Hasib al-Marwazi discovered the cotangent, and produced tables of tangents and cotangents. [32] [33] Muhammad ibn Jābir al-Harrānī al-Battānī (853–929) discovered the reciprocal functions of secant and cosecant, and produced the first table of cosecants for each degree from 1° to 90°. [33]

  5. Inverse hyperbolic functions - Wikipedia

    en.wikipedia.org/wiki/Inverse_hyperbolic_functions

    There are six in common use: inverse hyperbolic sine, inverse hyperbolic cosine, inverse hyperbolic tangent, inverse hyperbolic cosecant, inverse hyperbolic secant, and inverse hyperbolic cotangent. They are commonly denoted by the symbols for the hyperbolic functions, prefixed with arc- or ar- , or with a superscript − 1 {\displaystyle {-1 ...

  6. Pythagorean trigonometric identity - Wikipedia

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

    In this way, this trigonometric identity involving the tangent and the secant follows from the Pythagorean theorem. The angle opposite the leg of length 1 (this angle can be labeled φ = π/2 − θ) has cotangent equal to the length of the other leg, and cosecant equal to the length of the hypotenuse. In that way, this trigonometric identity ...

  7. Proofs of trigonometric identities - Wikipedia

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

    The sign of the square root needs to be chosen properly—note that if 2 π is added to θ, the quantities inside the square roots are unchanged, but the left-hand-sides of the equations change sign. Therefore, the correct sign to use depends on the value of θ.

  8. Category:Inverse trigonometric functions - Wikipedia

    en.wikipedia.org/wiki/Category:Inverse...

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  9. Mnemonics in trigonometry - Wikipedia

    en.wikipedia.org/wiki/Mnemonics_in_trigonometry

    Quadrant 3 (angles from 180 to 270 degrees, or π to 3π/2 radians): Tangent and cotangent functions are positive in this quadrant. Quadrant 4 (angles from 270 to 360 degrees, or 3π/2 to 2π radians): Cosine and secant functions are positive in this quadrant. Other mnemonics include: All Stations To Central [6] All Silly Tom Cats [6]