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Pycol can be used by students to compute trigonometric functions,(Sine,Cosine,Tangent,Cosecant,Secant, and Cotangent) of an angle(X) expressed in degrees rather than radians, since this is not available in Python math or cmath modules. Yet it is a standard method of measuring such ratios at colleges,universities and all mathematics books including Calculus. Pycol can also be used to express angles from degrees into radians and vice versa, and into degrees, minutes, and seconds

Python, 268 lines
 ``` 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 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268``` ```#On the name of ALLAH and may the blessing and peace of Allah #be upon the Messenger of Allah Mohamed Salla Allahu Aliahi Wassalam. #Author : Fouad Teniou #Date : 24/07/08 #versionl :2.4 import math as m import re #################################################################################################### # Degree measure: There are 360 degrees in an angle of one revolution. # Degrees are divided into 60 minutes and minutes are divided into 60 seconds. # Radian measure: 360 degrees is equal to 2(Pi) radians and 180 degrees is equal to Pi(3.14159rad) # Sine, Cosine ,Tangent , Cosecant, Secant, and Cotangent are trigonometric functions which could be # calculated for a given angle . #################################################################################################### class Pycol: def __init__(self,other,name='',value=0) #Initialize self.other = other self.name = name self.value = value def switch(self): cable = {30:(chr(244)+'/6'), 45:(chr(244 )+'/4'),60:( chr(244 )+ '/3'), 90:(chr(244)+'/2'), 120 :('2'+chr(244)+'/3'),135 :('3'+ chr(244) +'/4'), 150:('5'+chr(244)+'/6'), 180:(chr(244)),270:('3'+chr(244)+'/2'),360:('2'+chr(244))} #Make a dictionary if cable.has_key(self.other): #Step through rest and fetch dictionary values by their keys return cable [self.other] #Return Keys values def __mul__(self}: return self.value * self.other def __repr__(self): #test and Print if self.__class__.__name__ == "Degrees" or self.__class__.__name__ == "Radians": return ("\n %s(%s) = %s" % (self.__class__.__name__,self.__class__.__name__,self.other,self.__class__.__name__,str(Pycol.switch(self)[:]),self.compute)) else: return ("\n \d+)\.(\d*)", str("%2.2f" % self.other)) b = re.match(r"(?P\d+)\.(\d*)", "%2.2f" % float(str(float(a.group(2))*0.6))) c = re.match(r"(?P\d+)\.(\d*)", "%2.2f" % float(str(float(b.group(2))*0.6))) if Pycol.switch(self): print ('\n\t\t\t' + str(self.other)+ " deg" +" = " + a.group(1)+chr(248)+' '+b.group(1)+"'"+ ' '+ c.group(1)+'"'+"=" +("%2.5f" % float(Pyeol.__mul__(self)))+"rad"+" <--> "+ str(Pycol.switch(self)[:])) else: print ('\n\t\t\t' + str(self.other)+ " deg"+" = " + a.group(1)+chr(248)+' '+b.group(1)+"'"+' ' + c.group(1)+'"'+" = " +("%2.5f" % float(Pycol.__mul__(self)))+"rad") class Radians(Pycol): #Inherit def __init__(self,other): Pycol.__init__(self,other,'Degrees', 180/m.pi) #Run Pycol init def adapt(self): a = re.match(r"(?P\d+)\.(\d*)" , str( "%2.2f" % float(Pycol.__mul__(self)))) b = re.match(r"(?P\d+)\.(\d*)" ,"%2.2f" % float(str(float(a.group(2))*0.6))) c = re.match(r"(?P\d+)\.(\d*)" , "%2.2f" % float(str(float(b.group(2))*0.6))) print ('\n\t\t\t' + "%2.5f" % float(str(self.other)) + " rad" + " = "+"%2.2f" % float(Pycol.__mul__(self))+ " deg"+" = " + a.group(1)+chr(248)+' '+b.group(1)+"'"+'' +c.group(1)+ '"') class sin(Degrees): #Inherit def __init__(self,other}: Degrees.__init__(self,other) if self.other % 180 == 0 :#sin(X)=sin(X + 2Pi)=sin(X-2Pi),sin(0)=sin(180)=... self.compute = 0.0 else: self.compute = m.sin(Pycol.__mul__(self)) # sin(X)=Side opposite(X)/hypotenuse #X: given angle in degrees class sec(sin): def __init__(self,other): Degrees.__init__(self,other) if m.sqrt((1-((m.sin(Pycol.__mul__(self))**2)))) == 0: #sin**2(X) +cos**2(X)=1 self.compute = 'Division by Zero indefinebale' #Obtained from applying Theorem of Pythagoras else: #and using the sin(X) and cos(X) defInitions self.compute = 1/m.cos(Pycol.__mul__(self)) # sec(X)=1/cos(X) class cos(sec): def __init__(self,other): #Inherit Degrees.__init__(self,other) if self.other %90 == 0 and self.other %180 !=0:#cos(X)=cos(X +2Pi)=cos(X-2Pi),cos(90)=cos(270) =... self.compute = 0.0 else: self.compute = m.cos(Pycol.__mul__(self))# cos(X)= side adjacent to (X)/hypotcnus class csc(cos): def __init__(self,other): Degrees.__init__(self,other) if m.sqrt((1-((m.cos(Pycol.__mul__(self))**2)))) == 0: self.compute = 'Division by zero indefineable' else : self.compute = 1/m.sin(Pycol.__mul__(self)) #csc(X)= 1/sin(X) class tan(csc): def __init__(self,other}: Degrees.__init__(self,other) if self.other % 180 == 0 : self.compute = 0.0 elif m.sqrt((1-((m.sin(Pycol.__mul__(self))**2)))) == 0: # sin**2(X) +cos**2(X)=1 self.compute = 'Division by zero indefinebale' # Obtained from applying Theorem of Pythagoras else: #and using the sin(X} and cos(X) definitions self.compute = m.sin(Pycol.__mul__(self))/m.cos(Pycol.__mul__(self)) #tan(X)=sin(X)/cos(X) class cot(tan): def __init__(self,other): Degrees.__init__(self,other) if m.sqrt((1-((m.cos(Pyco1.__mul__(self))**2))))==0: # sin**2(X) +cos**2(X)=1 self.compute = 'Division by zero indefinebale' elif self.other %90 ==0 and self.other % 180 !=0: self.compute = 0.0 else: self.compute =1/(m.sin(Pycol.__mul__(self))/m.cos(Pycol.__mul__(self))) #cot(X)= 1/tan(X) if __name__ == '__main__': for i in (0,30,45,60,90,120,135,150,180,270,360): a = Degrees (i) print a a.adapt() b = Radians (6.283185307) print b b.adapt() for i in range(0,105,15): print sin(i) print cos(i) print tan(i) print csc(i) print sec(i) print cot(i) ---------------------------------------------------------------------------------- #alternatively students can use DOS and run the following # if __name__=='__main__""" instead of the above to compute their trigonometric # functions or converting methods if __name__ =='__main__': while 1: y=raw_input("\nPlease enter the function's name,'sin,cos,tan,sec,csc,cot'\nor a converting method 'deg,rad'\nor any key to exit\n") x=raw_input("Please enter the angle's value.\n") if y=='deg': a = Degrees(float(x)) a.adapt() elif y=='rad': a = Radians(float(x)) a.adapt() elif y=='sin': print sin(int(x)) elif y=='cos': print cos(int(x)) elif y=='tan': print tan(int(x)) elif y=='sec': print sec(int(x)) elif y=='csc': print csc(int(x)) elif y=='cot': print cot(int(x)) else: break ######################################################################################### #Version : Python 3.2 #import math as m #import re #class Pycol: # def __init__(self,other,name='',value=0): #Initialize # self.other = other # self.name = name # self.value = value # def switch(self): # cable = {30:(chr(182)+'/6'),45:(chr(182)+'/4'),60:(chr(182)+'/3'), # 90:(chr(182)+'/2'),120:('2'+chr(182)+'/3'),135:('3'+chr(182)+'/4'), # 150:('5'+chr(182)+'/6'),180:(chr(182)), # 270:('3'+chr(182)+'/2'),360:('2'+chr(182))} #Make a dictionary # if self.other in cable: #Step through test and fetch #dictionary values by their keys # return cable [self.other] #Return Keys values # def __mul__(self): # return self.value * self.other # def __repr__(self): #test and Print # if self.__class__.__name__ == "Degrees" or self.__class__.__name__ == "Radians": # return ("\n %s (%s) = %s " % # (self.__class__.__name__,self.__class__.__name__,self.other,self.__class__.__name__,str(Pycol.switch(self)[:]),self.compute)) # else : # return ("\n \d+)\.(\d*)", str( "%2.2f" % self.other)) # b = re.match(r"(?P\d+)\.(\d*)","%2.2f" % float(str(float(a.group(2))*0.6))) # c = re.match(r"(?P\d+)\.(\d*)", "%2.2f" % float(str(float(b.group(2))*0.6))) # if Pycol.switch(self): # print(('\n\t\t\t' + str(self.other)+ " deg" +" = " + a.group(1)+chr(176)#+' '+b.group(1)+"'"+' ' + # c.group(1)+'"'+" = " +("%2.5f" % float(Pycol.__mul__(self)))+"rad"+" #<--> "+ str(Pycol.switch(self)[:]))) # else : # print(('\n\t\t\t' + str(self.other)+ " deg" +" = " + a.group(1)+chr(176)#+' '+b.group(1)+"'"+' ' + # c.group(1)+'"'+" = " +("%2.5f" % float(Pycol.__mul__(self)))+"rad")) # #class Radians(Pycol): #Inherit # def __init__(self,other): # Pycol.__init__(self,other,'Degrees',180/m.pi) #Run Pycol init # def adapt(self): # a = re.match(r"(?P\d+)\.(\d*)", str( "%2.2f" % float(Pycol.__mul__(self)))) # b = re.match(r"(?P\d+)\.(\d*)","%2.2f" % float(str(float(a.group(2))*0.6))) # c = re.match(r"(?P\d+)\.(\d*)", "%2.2f" % float(str(float(b.group(2))*0.6))) # print(('\n\t\t\t' + "%2.5f" % float(str(self.other)) + " rad" + " = "+"%2.2f" % #float(Pycol.__mul__(self))+ # " deg"+" = " + a.group(1)+chr(176)+' '+b.group(1)+"'"+' ' +c.group(1)#+'"')) #class sin(Degrees): #Inherit # def __init__(self,other): # Degrees.__init__(self,other) # if self.other % 180 == 0 : #sin(X)=sin(X + 2Pi)#=sin(X-2Pi),sin(0)=sin(180)=... # self.compute = 0.0 # else: # self.compute = m.sin(Pycol.__mul__(self)) # sin(X)=Side #opposite(X)/hypotenuse # #X: given angle in #degrees #class sec(sin): #Inherit # def __init__(self,other): # Degrees.__init__(self,other) # if m.sqrt((1-((m.sin(Pycol.__mul__(self))**2)))) == 0: # sin**2(X) +cos**2(X)=1 # self.compute = 'Division by zero indefinebale' #Obtained from #applying Theorem of Pythagoras # else : #and using the sin(X) and cos(X) definitions # self.compute = 1/m.cos(Pycol.__mul__(self)) # sec(X)=1/cos(X) # #class cos(sec): #Inherit # def __init__(self,other): # Degrees.__init__(self,other) # if self.other %90 ==0 and self.other %180 !=0: #cos(X)=cos(X + 2Pi)#=cos(X-2Pi),cos(90)=cos(270) =... # self.compute = 0.0 # else : # self.compute = m.cos(Pycol.__mul__(self)) # cos(X)= side #adjacent to (X)/hypotenus #class csc(cos): # def __init__(self,other): # Degrees.__init__(self,other) # if m.sqrt((1-((m.cos(Pycol.__mul__(self))**2)))) == 0: # self.compute = 'Division by zero indefinebale' # else : # self.compute = 1/m.sin(Pycol.__mul__(self)) #csc(X)= 1/sin(X) #class tan(csc): # def __init__(self,other): # Degrees.__init__(self,other) # if self.other % 180 == 0 : # self.compute = 0.0 # elif m.sqrt((1-((m.sin(Pycol.__mul__(self))**2)))) == 0: # sin**2(X) +cos**2(X)=1 # self.compute = 'Division by zero indefinebale' #Obtained from #applying Theorem of Pythagoras # else: #and using the sin(X) and cos(X) definitions # self.compute = m.sin(Pycol.__mul__(self))/m.cos(Pycol.__mul__(self)) #tan(X)=sin(X)/cos(X) # #class cot(tan): # def __init__(self,other): # Degrees.__init__(self,other) # if m.sqrt((1-((m.cos(Pycol.__mul__(self))**2)))) == 0: # sin**2(X) +cos**2(X)=1 # self.compute = 'Division by zero indefinebale' # elif self.other %90 ==0 and self.other %180 !=0: # self.compute = 0.0 # else : # self.compute= 1/(m.sin(Pycol.__mul__(self))/m.cos(Pycol.__mul__(self))) #cot(X)=1/tan(X) ```

Justin Shaw 13 years, 4 months ago

Wow, That is a lot of infrastructure to handle degrees! Here is what I do. My default unit is radians (you can make your default unit whatever you want). Then I define constants that convert to/from my default unit.

#### define conversion constants

RAD = 1.; DEG = pi/180

#### convert back by dividing

theta_deg = acos(sqrt(2)/2) / DEG # convert answer into degrees

#### works every time!

Fouad Teniou (author) 13 years, 4 months ago

I read in different groups discussions that people were confused using radians instead of degrees while using trigonometric ratios and I wrote Pycol just for the purpose and it is a great experience try it yourself

 Created by Fouad Teniou on Thu, 24 Jul 2008 (MIT)

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