Module angle_sc::trig

The trig module contains functions for performing accurate trigonometry calculations.

The accuracy of the libm::sin function is poor for angles >= π/4 and the accuracy of the libm::cos function is poor for small angles, i.e., < π/4. So sin π/4 is explicitly set to 1/√2 and cos values are calculated from sin values using Pythagoras’ theorem.

The sincos function accurately calculates the sine and cosine of angles in radians by using remquo to reduce an angle into the range: -π/4 <= angle <= π/4; and its quadrant: along the positive or negative, x or y axis of the unit circle.
The sincos_diff function reduces the round-off error of the difference of two angles in radians using the 2Sum algorithm.

The sincosd function is the degrees equivalent of sincos and sincosd_diff is the degrees equivalent of sincos_diff.

The sines and cosines of angles are represented by the UnitNegRange struct which ensures that they lie in the range:
-1.0 <= value <= 1.0.

The functions arctan2 and arctan2d are the reciprocal of sincos and sincosd, transforming sine and cosines of angles into radians or degrees respectively.

The module contains the other trigonometric functions: tan, cot, sec and csc as functions taking sin and/or cos and returning an Option<f64> to protect against divide by zero.

The module also contains functions for:

• angle sum and difference identities;
• half-angle formulae;
• and the spherical law of cosines.

Structs

• UnitNegRange
  The UnitNegRange newtype an f64.
  A valid UnitNegRange value lies between -1.0 and +1.0 inclusive.

Constants

• COS_30_DEGREES
  The cosine of 30 degrees: √3/2
• MAX_COS_ANGLE_IS_ONE
  The maximum angle in Radians where: swap_sin_cos(libm::sin(value)) == 1.0
• MAX_LINEAR_SIN_ANGLE
  The maximum angle in Radians where: libm::sin(value) == value
• SQRT_3
  core::f64::consts::SQRT_3 is currently a nightly-only experimental API,
  see https://doc.rust-lang.org/core/f64/consts/constant.SQRT_3.html
• SQ_EPSILON
  ε * ε, a very small number.

Functions

• arctan2
  Accurately calculate an angle in Radians from its sine and cosine.
• arctan2d
  Accurately calculate an angle in Degrees from its sine and cosine.
• calculate_adjacent_length
  Calculates the length of the other side in a right angled triangle, given the length of one side and the hypotenuse.
  See: Pythagorean theorem
• cosine
  Calculate the cosine of an angle in Radians using the sine of the angle.
  Corrects cos π/4 to 1/√2.
• cosine_diff
  Calculate the cosine of the difference of two angles: a - b.
  See: angle sum and difference identities.
• cosine_from_sine
  Calculate the cosine of an angle from it’s sine and the sign of the cosine.
  See: swap_sin_cos.
• cosine_sum
  Calculate the cosine of the sum of two angles: a + b.
  See: angle sum and difference identities.
• cot
  The cotangent of an angle.
• csc
  The cosecant of an angle.
• sec
  The secant of an angle.
• sincos
  Calculate the sine and cosine of an angle from a value in Radians.
  Note: calculates the cosine of the angle from its sine and overrides both the sine and cosine for π/4 to their correct values: 1/√2
• sincos_diff
  Calculate the sine and cosine of an angle from the difference of a pair of values in Radians.
  Note: calculates the cosine of the angle from its sine and overrides the sine and cosine for π/4 to their correct values: 1/√2
• sincosd
  Calculate the sine and cosine of an angle from a value in Degrees.
  Note: calculates the cosine of the angle from its sine and overrides the sine and cosine for ±30° and ±45° to their correct values.
• sincosd_diff
  Calculate the sine and cosine of an angle from the difference of a pair of values in Degrees.
  Note: calculates the cosine of the angle from its sine and overrides the sine and cosine for ±30° and ±45° to their correct values.
• sine
  Calculate the sine of an angle in Radians.
  Corrects sin ±π/4 to ±1/√2.
• sine_diff
  Calculate the sine of the difference of two angles: a - b.
  See: angle sum and difference identities.
• sine_sum
  Calculate the sine of the sum of two angles: a + b.
  See: angle sum and difference identities.
• spherical_adjacent_length
  Calculates the length of the other side in a right angled spherical triangle, given the length of one side and the hypotenuse.
  See: Spherical law of cosines
• spherical_cosine_rule
  Calculate the length of the adjacent side of a right angled spherical triangle, given the cosine of the angle and length of the hypotenuse.
  See: Spherical law of cosines
• spherical_hypotenuse_length
  Calculates the length of the hypotenuse in a right angled spherical triangle, given the length of both sides.
  See: Spherical law of cosines
• sq_cosine_half
  Square of the cosine of half the Angle.
  See: Half-angle formulae
• sq_sine_half
  Square of the sine of half the Angle.
  See: Half-angle formulae
• swap_sin_cos
  Swap the sine into the cosine of an angle and vice versa.
  Uses the identity sin² + cos² = 1.
  See: Pythagorean identities
• tan
  The tangent of an angle.