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  2. Exact trigonometric values - Wikipedia

    en.wikipedia.org/wiki/Exact_trigonometric_values

    The values of sine and cosine of 30 and 60 degrees are derived by analysis of the equilateral triangle. In an equilateral triangle, the 3 angles are equal and sum to 180°, therefore each corner angle is 60°. Bisecting one corner, the special right triangle with angles 30-60-90 is obtained.

  3. List of trigonometric identities - Wikipedia

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

    A formula for computing the trigonometric identities for the one-third angle exists, but it requires finding the zeroes of the cubic equation 4x 3 − 3x + d = 0, where is the value of the cosine function at the one-third angle and d is the known value of the cosine function at the full angle.

  4. 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.

  5. 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.

  6. Sine and cosine - Wikipedia

    en.wikipedia.org/wiki/Sine_and_cosine

    cos(x) Degrees Radians Gradians Turns Exact Decimal Exact Decimal 0° 0 0 g: 0 0 0 1 1 30° ⁠ 1 / 6 ⁠ π ⁠33 + 1 / 3 ⁠ g ⁠ 1 / 12 ⁠ ⁠ 1 / 2 ⁠ 0.5 0.8660 45° ⁠ 1 / 4 ⁠ π: 50 g ⁠ 1 / 8 ⁠ 0.7071 0.7071 60° ⁠ 1 / 3 ⁠ π ⁠66 + 2 / 3 ⁠ g ⁠ 1 / 6 ⁠

  7. Proofs of trigonometric identities - Wikipedia

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

    1.5.2 Cosine. 1.5.3 Tangent and cotangent. ... Two angles whose sum is π/2 radians (90 degrees) are complementary. In the diagram, the angles at vertices A and B are ...

  8. Radian - Wikipedia

    en.wikipedia.org/wiki/Radian

    One radian is defined as the angle at the center of a circle in a plane that subtends an arc whose length equals the radius of the circle. [6] More generally, the magnitude in radians of a subtended angle is equal to the ratio of the arc length to the radius of the circle; that is, =, where θ is the magnitude in radians of the subtended angle, s is arc length, and r is radius.

  9. Trigonometric tables - Wikipedia

    en.wikipedia.org/wiki/Trigonometric_tables

    For example, the cosine and sine of 2π ⋅ 5/37 are the real and imaginary parts, respectively, of the 5th power of the 37th root of unity cos(2π/37) + sin(2π/37)i, which is a root of the degree-37 polynomial x 37 − 1.