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  2. 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.

  3. Machin-like formula - Wikipedia

    en.wikipedia.org/wiki/Machin-like_formula

    If = then ⁡ is 45 degrees or radians. This means that if the real part and complex part are equal then the arctangent will equal . Since the arctangent of one has a very slow convergence rate if we find two complex numbers that when multiplied will result in the same real and imaginary part we will have a Machin-like formula.

  4. Inverse trigonometric functions - Wikipedia

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

    Or, "the arc whose cosine is x" is the same as "the angle whose cosine is x", because the length of the arc of the circle in radii is the same as the measurement of the angle in radians. [5] In computer programming languages, the inverse trigonometric functions are often called by the abbreviated forms asin, acos, atan. [6]

  5. Exact trigonometric values - Wikipedia

    en.wikipedia.org/wiki/Exact_trigonometric_values

    As discussed in § Constructibility, only certain angles that are rational multiples of radians have trigonometric values that can be expressed with square roots. The angle 1°, being π / 180 = π / ( 2 2 ⋅ 3 2 ⋅ 5 ) {\displaystyle \pi /180=\pi /(2^{2}\cdot 3^{2}\cdot 5)} radians, has a repeated factor of 3 in the denominator and therefore ...

  6. Small-angle approximation - Wikipedia

    en.wikipedia.org/wiki/Small-angle_approximation

    provided the angle is measured in radians. Angles measured in degrees must first be converted to radians by multiplying them by ⁠ / ⁠. These approximations have a wide range of uses in branches of physics and engineering, including mechanics, electromagnetism, optics, cartography, astronomy, and computer science.

  7. Trigonometric functions - Wikipedia

    en.wikipedia.org/wiki/Trigonometric_functions

    Basis of trigonometry: if two right triangles have equal acute angles, they are similar, so their corresponding side lengths are proportional.. In mathematics, the trigonometric functions (also called circular functions, angle functions or goniometric functions) [1] are real functions which relate an angle of a right-angled triangle to ratios of two side lengths.

  8. Mnemonics in trigonometry - Wikipedia

    en.wikipedia.org/wiki/Mnemonics_in_trigonometry

    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] Add Sugar To Coffee [6] All Science Teachers (are) Crazy [7] A Smart Trig Class [8] All Schools Torture Children [5] Awful Stinky Trig Course [5]

  9. Proofs of trigonometric identities - Wikipedia

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

    Two angles whose sum is π/2 radians (90 degrees) are complementary. In the diagram, the angles at vertices A and B are complementary, so we can exchange a and b, and change θ to π/2 − θ, obtaining: ⁡ (/) = ⁡