Function cos

src/compute-engine/interval/trigonometric.ts:57–82

(x: Interval | IntervalResult)

}

/**
 * Cosine of an interval.
 *
 * Cos is bounded [-1, 1] and periodic with extrema at n*pi.
 */
export function cos(x: Interval | IntervalResult): IntervalResult {
  const unwrapped = unwrapOrPropagate(x);
  if (!Array.isArray(unwrapped)) return unwrapped;
  const [xVal] = unwrapped;
  // Wide interval spans full range
  if (xVal.hi - xVal.lo >= TWO_PI) {
    return ok({ lo: -1, hi: 1 });
  }

  // Endpoint values
  const cosLo = Math.cos(xVal.lo);
  const cosHi = Math.cos(xVal.hi);
  let lo = Math.min(cosLo, cosHi);
  let hi = Math.max(cosLo, cosHi);

  // Check for maximum at 2n*pi (including 0)
  if (containsExtremum(xVal, 0, TWO_PI)) {
    hi = 1;
  }
  // Check for minimum at pi + 2n*pi
  if (containsExtremum(xVal, PI, TWO_PI)) {
    lo = -1;
  }