first set

Author: SREEHARI1994

wee7marks.PNG

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+import math
+def cos(n):
+	return math.cos(n)
+def tan(n):
+	return math.tan(n)
+
+def cartesian_to_polar(x,y):
+	# Calculating radius
+	radius = math.sqrt( x * x + y * y )
+	# Calculating angle (theta) in radian
+	theta = math.atan(y/x)
+	if x<0 and not y<0:
+		theta=math.pi+theta
+	return radius,theta
+
+def polar_to_cartesian(radius,theta):
+	x = radius * math.cos(theta)
+	y = radius * math.sin(theta)
+	return x,y
+
+if __name__=="__main__":
+	pi=math.pi
+	#1st question
+	a=pi/4
+	print(f"1) {math.sin(a):.2f}")
+	#2nd question
+	a=pi/2
+	print(f"2) {math.sin(a):.2f}")
+	#3rd question
+	a=pi/3
+	print(f"3) {math.sin(a):.2f}")
+	#4th question
+	a=0
+	print(f"4) {math.sin(a):.2f}")
+	#fifth question
+	b=0
+	print(f"5) {math.cos(b):.2f}")
+	#questions 6-10
+	quantity={6:pi/3,7:3*pi/4,8:-pi/6,9:2*pi/3,10:5*pi/4}
+	for i in range(6,11):
+		if i in[6,7,8]:
+			print(f"{i} {cos(quantity[i]): .2f}")
+		else:
+			print(f"{i} {tan(quantity[i]): .2f}")
+	#questions 11-20
+	quantity={11:[3,4],12:[math.sqrt(3),1],13:[-2,2],14:[0,1],15:[5,12],16:[1,0],17:[3,pi/4],18:[3,9*pi/4],
+				19:[5,2*pi/3],20:[2,11*pi/6]}
+	for i in range(11,21):
+		
+		if i in (11,12,13,15):
+			
+			print(f"{i} {cartesian_to_polar(*quantity[i])}")
+		elif i==14:
+			print(f"{i} {pi/2}")
+		else:
+			print(f"{i} {polar_to_cartesian(*quantity[i])}")
+
+
+
+	
+

week1.py

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+import math
+import cmath
+from week1 import cartesian_to_polar as cf
+
+print(cf(-15,-8))
+print(cf(math.sqrt(1/3),math.sqrt(2/3)))
+
+#multiplying complex numbers
+
+def cmultiply(a,b):
+    return a*b
+print(cmultiply(2-7j,3-2j))
+
+#magnitude of complex numbers
+
+print(abs(complex(5,-12)))
+
+#converting complex numbers to polar form
+def cm2polar(a):
+    """
+    converts the complex number into polar form,returns a tuple r,phi where r is 
+    modulus, phi is phase angle
+    """
+    return cmath.polar(a)
+
+def polar_display(a,b):
+    """
+    displaying the polar form of complex number a+ib in conventional form
+    """
+    q=math.pi/b
+    return f"{a}e**iPI/{q}"
+
+r,phi=cm2polar(complex(0,5))
+print(polar_display(r,phi))

week3.py

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+def vector_inner_product(a,b):
+    if len(a)!=len(b):
+        return "The two vectors should be of same dimensions"
+    product=0
+    for i in range(len(a)):
+        product=product+a[i]*b[i]
+    return product
+
+def check_orthogonal(a,b):
+	if vector_inner_product(a,b)==0:
+		return True
+	else:
+		return False
+
+def linear_combination_len2(r,a,b):
+	"""
+	returns a linear combinations of vectors of length 2,solving by elimination
+	1st equation coefficients-
+	rightside=r[0]
+	x_coefficient=a[0]
+	y_coefficient=b[0]
+	2nd equation coefficients
+	rightside=r[1]
+	x_coefficient=a[1]
+	y_coefficient=b[1]
+	"""
+	original=(r[0],a[0],b[0])
+	if a[0]>=a[1]:
+		multiplier=a[0]/a[1]
+		r[1]=r[1]*multiplier
+		a[1]=a[1]*multiplier
+		b[1]=b[1]*multiplier
+	else:
+		multiplier=a[1]/a[0]
+		r[0]=multiplier*r[0]
+		a[0]=multiplier*a[0]
+		b[0]=multiplier*b[0]
+	
+	assert a[0]-a[1]==0
+	y=(r[0]-r[1])/(b[0]-b[1])
+	x=(original[0]-y*original[2])/original[1]
+	return x,y
+
+def transpose(p):
+	"""returns the transpose t of a matrix p"""
+	t=[]
+	for i in range(len(p)):
+		row=[]
+		for j in range(len(p[i])):
+			row.append(p[j][i])
+		t.append(row)
+	return t
+
+def matrix_multiply(a,b):
+	res=[]
+	for row in a:
+		r=[]
+		for column in b:
+			r.append(vector_inner_product(row,column))
+		res.append(r)
+	return res
+			
+
+		
+
+
+if __name__ == "__main__":
+	print("1) ",vector_inner_product([5,2],[6,8]))
+	print("2) ",vector_inner_product([3,10],[1,7]))
+	print("3) ",vector_inner_product([1,-2,4],[2,3,3]))
+	print("4) ",check_orthogonal([1,5],[-5,1]))
+	print("5) ",check_orthogonal([3,6,2],[1,4,3]))
+	print("6) ", linear_combination_len2([5,5],[1,2],[3,1]))
+	print("7) ", linear_combination_len2([-7,16],[1,2],[3,1]))
+	print("8 ",matrix_multiply([[2,3],[1,4]],[[3,-2]]))
+	print("9 ",matrix_multiply([[1,4],[0,5]],[[1,1]]))
+	print("10 ",matrix_multiply([[-2,6],[9,4]],[[3,-5],[3,1]]))
+
+
+

week4.py

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+#My solutions to the homework assignments of week7
+"""
+1)option 2
+2)3
+3)1
+4)color
+5)seashells==3
+6)2
+7)2 4
+8)4
+9)1
+10)x*y
+11)0
+12)2
+13)year age
+14)3
+15)4
+16)2
+17)1
+"""