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
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#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 <Pycol : Express %s %s into (Degrees + minutes + seconds) and %s " %
(self.other,self.__class__.__name__,self.name))
else:
if Pycol.switch(self): #Test if self.other in dictionary keys
return ("\n <Pycol : Compute %s function \t %s (%s) <--> %s(%s) = %s" %
(self.__class__.__name__,self.__class__.__name__,self.other,self.__class__.__name__,str(Pycol.switch(self)[:]),self.compute))
else:
return ("\n <Pycol : Compute %s function \t %s (%s) = %s" %
(self.__class__.__name__,self.__class__.__name__,self.other,self.compute))
class Degrees(Pycol):
def __init__(self,other): #Inherit .
Pycol.__init__(self,other,'Radians',m.pi/180) #Run Pycol init
def adapt(self):
a = re.match(r"(?P<int>\d+)\.(\d*)", str("%2.2f" % self.other))
b = re.match(r"(?P<int>\d+)\.(\d*)", "%2.2f" % float(str(float(a.group(2))*0.6)))
c = re.match(r"(?P<int>\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<int>\d+)\.(\d*)" , str( "%2.2f" % float(Pycol.__mul__(self))))
b = re.match(r"(?P<int>\d+)\.(\d*)" ,"%2.2f" % float(str(float(a.group(2))*0.6)))
c = re.match(r"(?P<int>\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 <Pycol : Express %s %s into (Degrees + minutes + seconds)and %#s " %
# (self.other,self.__class__.__name__,self.name))
# else:
# if Pycol.switch(self): #Test if selfother #in dictionary keys
# return ("\n <Pycol : Compute %s function \t %s (%s) <--> %s (%s) = %s " %
# (self.__class__.__name__,self.__class__.__name__,self.other,self.__class__.__name__,str(Pycol.switch(self)[:]),self.compute))
# else :
# return ("\n <Pycol : Compute %s function \t %s (%s) = %s" %
# (self.__class__.__name__,self.__class__.__name__,self.other,self.compute))
#class Degrees(Pycol):
# def __init__(self,other): #Inherit
# Pycol.__init__(self,other,'Radians',m.pi/180) #Run Pycol init
# def adapt(self):
# a = re.match(r"(?P<int>\d+)\.(\d*)", str( "%2.2f" % self.other))
# b = re.match(r"(?P<int>\d+)\.(\d*)","%2.2f" % float(str(float(a.group(2))*0.6)))
# c = re.match(r"(?P<int>\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<int>\d+)\.(\d*)", str( "%2.2f" % float(Pycol.__mul__(self))))
# b = re.match(r"(?P<int>\d+)\.(\d*)","%2.2f" % float(str(float(a.group(2))*0.6)))
# c = re.match(r"(?P<int>\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)
|
Tags: algorithms
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
Try them out
print sin(90DEG); print sin(2pi*RAD)
convert back by dividing
theta_deg = acos(sqrt(2)/2) / DEG # convert answer into degrees
and in radians
theta_rad acos(sqrt(2)/2) / RAD # 'convert' answer into radians
works every time!
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