1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
|
[vset VERSION 1.1]
[manpage_begin math::trig n [vset VERSION]]
[keywords math trigonometry]
[copyright {2018 Arjen Markus}]
[moddesc {Tcl Math Library}]
[titledesc {Trigonometric anf hyperbolic functions}]
[category Mathematics]
[require Tcl "8.5 9"]
[require math::trig [vset VERSION]]
[description]
[para]
The [term math::trig] package defines a set of trigonomic and hyperbolic functions
and their inverses. In addition it defines versions of the trigonomic functions
that take arguments in degrees instead of radians.
[para]
For easy use these functions may be imported into the [term tcl::mathfunc] namespace,
so that they can be used directly in the [term expr] command.
[section "FUNCTIONS"]
The functions [term radian_reduced] and [term degree_reduced] return a reduced angle, in
respectively radians and degrees, in the intervals [lb]0, 2pi) and [lb]0, 360):
[list_begin definitions]
[call [cmd ::math::trig::radian_reduced] [arg angle]]
Return the equivalent angle in the interval [lb]0, 2pi).
[list_begin arguments]
[arg_def float angle] Angle (in radians)
[list_end]
[call [cmd ::math::trig::degree_reduced] [arg angle]]
Return the equivalent angle in the interval [lb]0, 360).
[list_begin arguments]
[arg_def float angle] Angle (in degrees)
[list_end]
[list_end]
The following trigonomic functions are defined in addition to the ones defined
in the [term expr] command:
[list_begin definitions]
[call [cmd ::math::trig::cosec] [arg angle]]
Calculate the cosecant of the angle (1/cos(angle))
[list_begin arguments]
[arg_def float angle] Angle (in radians)
[list_end]
[call [cmd ::math::trig::sec] [arg angle]]
Calculate the secant of the angle (1/sin(angle))
[list_begin arguments]
[arg_def float angle] Angle (in radians)
[list_end]
[call [cmd ::math::trig::cotan] [arg angle]]
Calculate the cotangent of the angle (1/tan(angle))
[list_begin arguments]
[arg_def float angle] Angle (in radians)
[list_end]
[list_end]
For these functions also the inverses are defined:
[list_begin definitions]
[call [cmd ::math::trig::acosec] [arg value]]
Calculate the arc cosecant of the value
[list_begin arguments]
[arg_def float value] Value of the argument
[list_end]
[call [cmd ::math::trig::asec] [arg value]]
Calculate the arc secant of the value
[list_begin arguments]
[arg_def float value] Value of the argument
[list_end]
[call [cmd ::math::trig::acotan] [arg value]]
Calculate the arc cotangent of the value
[list_begin arguments]
[arg_def float value] Value of the argument
[list_end]
[list_end]
The following hyperbolic and inverse hyperbolic functions are defined:
[list_begin definitions]
[call [cmd ::math::trig::cosech] [arg value]]
Calculate the hyperbolic cosecant of the value (1/sinh(value))
[list_begin arguments]
[arg_def float value] Value of the argument
[list_end]
[call [cmd ::math::trig::sech] [arg value]]
Calculate the hyperbolic secant of the value (1/cosh(value))
[list_begin arguments]
[arg_def float value] Value of the argument
[list_end]
[call [cmd ::math::trig::cotanh] [arg value]]
Calculate the hyperbolic cotangent of the value (1/tanh(value))
[list_begin arguments]
[arg_def float value] Value of the argument
[list_end]
[call [cmd ::math::trig::asinh] [arg value]]
Calculate the arc hyperbolic sine of the value
[list_begin arguments]
[arg_def float value] Value of the argument
[list_end]
[call [cmd ::math::trig::acosh] [arg value]]
Calculate the arc hyperbolic cosine of the value
[list_begin arguments]
[arg_def float value] Value of the argument
[list_end]
[call [cmd ::math::trig::atanh] [arg value]]
Calculate the arc hyperbolic tangent of the value
[list_begin arguments]
[arg_def float value] Value of the argument
[list_end]
[call [cmd ::math::trig::acosech] [arg value]]
Calculate the arc hyperbolic cosecant of the value
[list_begin arguments]
[arg_def float value] Value of the argument
[list_end]
[call [cmd ::math::trig::asech] [arg value]]
Calculate the arc hyperbolic secant of the value
[list_begin arguments]
[arg_def float value] Value of the argument
[list_end]
[call [cmd ::math::trig::acotanh] [arg value]]
Calculate the arc hyperbolic cotangent of the value
[list_begin arguments]
[arg_def float value] Value of the argument
[list_end]
[list_end]
The following versions of the common trigonometric functions and their
inverses are defined:
[list_begin definitions]
[call [cmd ::math::trig::sind] [arg angle]]
Calculate the sine of the angle (in degrees)
[list_begin arguments]
[arg_def float angle] Angle (in degrees)
[list_end]
[call [cmd ::math::trig::cosd] [arg angle]]
Calculate the cosine of the angle (in degrees)
[list_begin arguments]
[arg_def float angle] Angle (in radians)
[list_end]
[call [cmd ::math::trig::tand] [arg angle]]
Calculate the cotangent of the angle (in degrees)
[list_begin arguments]
[arg_def float angle] Angle (in degrees)
[list_end]
[call [cmd ::math::trig::cosecd] [arg angle]]
Calculate the cosecant of the angle (in degrees)
[list_begin arguments]
[arg_def float angle] Angle (in degrees)
[list_end]
[call [cmd ::math::trig::secd] [arg angle]]
Calculate the secant of the angle (in degrees)
[list_begin arguments]
[arg_def float angle] Angle (in degrees)
[list_end]
[call [cmd ::math::trig::cotand] [arg angle]]
Calculate the cotangent of the angle (in degrees)
[list_begin arguments]
[arg_def float angle] Angle (in degrees)
[list_end]
[list_end]
[vset CATEGORY {math :: trig}]
[include ../common-text/feedback.inc]
[manpage_end]
|
