Description of sin

sin		Programmers Guide
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Category:intervals,math

Component type:function

Prototype

template <class Tnum> interval<Tnum> sin(const interval<Tnum>& x) ;

Description

Computes the trigonometric sine of an interval. If the interval's left bound is not less than 0 or if its right bound is greater than 2*pi, then it will print
bad argument for restricted sine of [x,y]
where x and y are the bounds of the interval and will return NaN.

 distance_left = right(x) - piby2()
 distance_right = piby2() - left(x)
 sin(x) = 
 if (piby2 & x) != empty:
 [-1.0,1.0]                if sup(x & pi3by2) != 0 and inf(x & pi3by2) != 0
 [sin(sup(x),1.0]          if inf(distance_right) > sup(distance_left) 
 [sin(inf(x),1.0]          else if inf(distance_left) > sup(distance_right) 
 [sin(sup(x),1.0]          else if sin(inf(x)) > sin(sup(x)) 
 [sin(inf(x),1.0]          else
 if (pi3by2 & x) != empty:
 [-1.0,sin(sup(x))]        if inf(distance_right) > sup(distance_left)
 [-1.0,sin(inf(x))]        if inf(distance_left) > sup(distance_right)
 [-1.0,sin(sup(x))]        else if sin(sup(x)) > sin(left(x))
 [-1.0,sin(inf(x))]        else
 if sup(x) < inf(piby2) or inf(x) > sup(pi3by2):
 [sin(inf(x)),sin(sup(x))]
 else:
 [sin(sup(x)),sin(inf(x))]

Definition

interval.cct

Preconditions

Complexity

Example

In mathfunc.cc:

  cout << "A:" << A << endl << endl;
  cout << "Square     :" << sqr(A) << endl;
  cout << "Square Root:" << sqrt(A) << endl;
  cout << "Tangent    :" << tan(A) << endl;
  cout << "ArcTangent :" << atan(A) << endl;
  cout << "Sine       :" << sin(A) << endl;
  cout << "Cosine     :" << cos(A) << endl;
  cout << "Arcsine    :" << asin(A) << endl;
  cout << "Arcosine   :" << acos(A) << endl;
  cout << "Log        :" << log(A) << endl;
  cout << "Ln         :" << ln(A) << endl;
  cout << "Power (A^A):" << pow(A,A) << endl;
  cout << "Exponent   :" << exp(A) << endl;

Notes

See also