First-class functions: Difference between revisions
Content added Content deleted
(→{{header|REXX}}: Removed white space from many <math> tags - restoring visibility to Pi, fixing ill-formed HTML) |
|||
| Line 2,134: | Line 2,134: | ||
The reason why '''Asin[sin(n)]''' may not equal '''n''': |
The reason why '''Asin[sin(n)]''' may not equal '''n''': |
||
Each of the trigonometric functions is periodic in the real part of its argument, running through all its values twice in each interval of <big>2<big><math> |
Each of the trigonometric functions is periodic in the real part of its argument, running through all its values twice in each interval of <big>2<big><math>\pi</math></big></big>. |
||
'''Sine''' and '''cosecant''' begin their period at <big>2<big><math> |
'''Sine''' and '''cosecant''' begin their period at <big>2<big><math>\pi</math></big>k − <big><math>\pi</math></big>/2</big> (where <big>k</big> is an integer), finish it at <big>2<big><math>\pi</math></big>k + <big><math>\pi</math></big>/2</big>, and then reverse themselves over <big>2<big><math>\pi</math></big>k + <big><math>\pi</math></big>/2</big> ───► <big>2<big><math>\pi</math></big>k + 3<big><math>\pi</math></big>/2</big>. |
||
'''Cosine''' and '''secant''' begin their period at <big>2<big><math> |
'''Cosine''' and '''secant''' begin their period at <big>2<big><math>\pi</math></big>k</big>, finish it at <big>2<big><math>\pi</math></big>k + <big><math>\pi</math></big></big>, and then reverse themselves over <big>2<big><math>\pi</math></big>k + <big><math>\pi</math></big></big> ───► <big>2<big><math>\pi</math></big>k + 2<big><math> \pi </math></big></big>. |
||
'''Tangent''' begins its period at <big>2<big><math> |
'''Tangent''' begins its period at <big>2<big><math>\pi</math></big>k − <big><math>\pi</math></big>/2</big>, finishes it at <big>2<big><math>\pi</math></big>k + <big><math>\pi</math></big>/2</big>, and then repeats it (forward) over <big>2<big><math>\pi</math></big>k + <big><math>\pi</math></big>/2</big> ───► <big>2<big><math>\pi</math></big>k + 3<big><math>\pi</math></big>/2</big>. |
||
'''Cotangent''' begins its period at <big>2<big><math> |
'''Cotangent''' begins its period at <big>2<big><math>\pi</math></big>k</big>, finishes it at <big>2<big><math>\pi</math></big>k + <big><math>\pi</math></big></big>, and then repeats it (forward) over <big>2<big><math>\pi</math></big>k + <big><math>\pi</math></big></big> ───► <big>2<big><math>\pi</math></big>k + 2<big><math>\pi</math></big></big>. |
||
<br>The above text is from the Wikipedia webpage: http://en.wikipedia.org/wiki/Inverse_trigonometric_functions |
<br>The above text is from the Wikipedia webpage: http://en.wikipedia.org/wiki/Inverse_trigonometric_functions |
||