Lab1temp_151_24A

2/7/24, 12:32 AM Lab1temp_151_24A localhost:8890/nbconvert/html/Lab1temp_151_24A.ipynb?download=false 1/9 MATH 151 Lab 1 Put team members' names and section number here. Section 404 - Group 3 Lisa Pham, Coby Holley, Bradley White, Owen Koss, Redlin Krueger, Garret Worden Question 1 1a (8(ln(12.1) - ln(8.6))) / (2024 - 28^2) = 0.00220285967318215 1b In [ ]: import sympy as sp from sympy.plotting import ( plot , plot_parametric ) In [7]: from sympy import * a1 = ( 8 * ( ln ( 12.1 ) - ln ( 8.6 ))) / ( 2024 - 28 ** 2 ) print ( "(8(ln(12.1) - ln(8.6))) / (2024 - 28^2) =" , a1 )

2/7/24, 12:32 AM Lab1temp_151_24A localhost:8890/nbconvert/html/Lab1temp_151_24A.ipynb?download=false 2/9 sin(pi/2) + cos(3) = cos(3) + 1 Question 2 2a The identity holds for the value pi/3 In [6]: from sympy import * b1 = sin ( pi / 2 ) + cos ( 3 ) print ( "sin(pi/2) + cos(3) =" , b1 ) In [2]: import sympy as sp #define the function def identity ( x ): def side1 ( x ): ( sp . cos ( x )) ** 2 def side2 ( x ): .5 * ( 1 + sp . cos ( 2 * x )) if side1 ( x ) == side2 ( x ): print ( 'The identity holds for the value' , x ,) else : print ( 'The identity does not hold for the value' , x ,) #test the values identity (( sp . pi ) / 3 )

2/7/24, 12:32 AM Lab1temp_151_24A localhost:8890/nbconvert/html/Lab1temp_151_24A.ipynb?download=false 4/9 a + b: [1, 8] a - b: [3, -2] 3a - 5b: [11, -16] 3b a = [ 2 , 3 ] b = [ - 1 , 5 ] # Question 3 part A a_add_b = [ a [ i ] + b [ i ] for i in range ( len ( a ))] a_minus_b = [ a [ i ] - b [ i ] for i in range ( len ( a ))] a_minus_b_x3 = [ 3 * a [ i ] - 5 * b [ i ] for i in range ( len ( a ))] print ( "a + b:" , a_add_b ) print ( "a - b:" , a_minus_b ) print ( "3a - 5b:" , a_minus_b_x3 ) In [3]: import math # defining vectors a = [ 2 , 3 ] b = [ - 1 , 5 ] # Question 3 part A a_add_b = [ a [ i ] + b [ i ] for i in range ( len ( a ))] a_minus_b = [ a [ i ] - b [ i ] for i in range ( len ( a ))] a_minus_b_x3 = [ 3 * a [ i ] - 5 * b [ i ] for i in range ( len ( a ))] # Question 3 part B

2/7/24, 12:32 AM Lab1temp_151_24A localhost:8890/nbconvert/html/Lab1temp_151_24A.ipynb?download=false 5/9 Angle a makes relative to the x-axis (rads): 0.982793723247329 3c Unit vector of 3a - 5b: [0.5665288228870652, -0.8240419241993676] Question 4 4a angle_radians = math . atan2 ( a [ 1 ], a [ 0 ]) print ( "Angle a makes relative to the x-axis (rads):" , angle_radians ) In [10]: import math # defining vectors a = [ 2 , 3 ] b = [ - 1 , 5 ] a_minus_b_x3 = [ 3 * a [ i ] - 5 * b [ i ] for i in range ( len ( a ))] magnitude = math . sqrt ( a_minus_b_x3 [ 0 ] ** 2 + a_minus_b_x3 [ 1 ] ** 2 ) unit_vector = [ a_minus_b_x3 [ i ] / magnitude for i in range ( len ( a_minus_b_x3 print ( "Unit vector of 3a - 5b:" , unit_vector ) In [3]: from sympy import * # Given force vector F = 5i + 9j

2/7/24, 12:32 AM Lab1temp_151_24A localhost:8890/nbconvert/html/Lab1temp_151_24A.ipynb?download=false 7/9 Magnitude of the displacement vector: 2*sqrt(10) 4d work/dot product = 64 In [6]: from sympy import * # Given force vector F = 5i + 9j F = ( 5 , 9 ) initial_point = ( 3 , 4 ) final_point = ( 5 , 10 ) # (c) Magnitude of the displacement vector magnitude_displacement = sqrt ( displacement_vector [ 0 ] ** 2 + displacement_vec print ( f"Magnitude of the displacement vector: { magnitude_displacement }" ) In [34]: from sympy import * p = [ 2 , 6 ] F = [ 5 , 9 ] num = dot ( p , F ) print ( "work/dot product =" , num )

2/7/24, 12:32 AM Lab1temp_151_24A localhost:8890/nbconvert/html/Lab1temp_151_24A.ipynb?download=false 8/9 4e cos of angle = 64/(2*sqrt(10) + sqrt(106)) 4f In [36]: from sympy import * p = [ 2 , 6 ] F = [ 5 , 9 ] num = dot ( p , F ) mag_p = sqrt (( p [ 0 ] ** 2 ) + ( p [ 1 ] ** 2 )) mag_F = sqrt (( F [ 0 ] ** 2 ) + ( F [ 1 ] ** 2 )) cos_theta = num / ( mag_p + mag_F ) print ( 'cos of angle =' , cos_theta ) In [37]: from sympy import * p = [ 2 , 6 ] F = [ 5 , 9 ] num = dot ( p , F ) mag_p = sqrt (( p [ 0 ] ** 2 ) + ( p [ 1 ] ** 2 )) mag_F = sqrt (( F [ 0 ] ** 2 ) + ( F [ 1 ] ** 2 )) cos_theta = num / ( mag_p + mag_F )