1.2.B.sagews

from sympy import *
from sympy import N as Num

from mpmath import degrees, radians

# SI units:
m  = Symbol("m",  positive=True)
s  = Symbol("s",  positive=True)
kg = Symbol("kg", positive=True)


print("\n--- User input -----------------------")

# Derived units:
N = kg*m/s/s

# quantity =  factor times unit:
alpha = radians(30)
beta = radians(70)
F = 3 * N

n_sig = 3

def round(comp):
    # significant digits for rounding:
    comp = Num(comp/N, n_sig)
    return str(comp)

def write(comp):
    comp = round(comp)
    pprint(" &= " + comp + " \N")

print("\n--- a: -------------------------------")

ca = cos(alpha)
sa = sin(alpha)
F_x = F * ca
F_y = F * sa

for comp in [F_x, F_y]:
    write(comp)

print("\n--- b: -------------------------------")

gamma = beta - alpha

cg = cos(gamma)
sg = sin(gamma)
F_bx = F * cg
F_by = - F * sg

for comp in [F_bx, F_by]:
    write(comp)

print("\n--- c: -------------------------------")

dlt = pi - beta
eps = beta - alpha
sd = sin(dlt)
se = sin(eps)

F_g = F * se/sd
F_b = F * sa/sd

for comp in [F_g, F_b]:
    write(comp)

--- User input ----------------------- --- a: ------------------------------- &= 2.60 \N &= 1.50 \N --- b: ------------------------------- &= 2.30 \N &= -1.93 \N --- c: ------------------------------- &= 2.05 \N &= 1.60 \N