Why is sin 30 not equal to 0.5?

>>> sin 30
-0.9880316240928618

Because sin expects the angle in radians.

>>> sin (30/180 * pi)
0.49999999999999994

  (a) 2 ^ (3 ^ 4)
  (b) (2 / 3) / 4
  (c) 7 - (5 / 4)
  (d) (log 49) / 7

>>> logBase 2 32
5.0

Calculate the polar coordinates (r,θ) for Cartesian coordinates (x, y) = (–3,4).

>>> theta = atan2 4 (-3)
>>> x = -3
>>> y = 4
>>> θ = atan2 y x
>>> r = sqrt (x**2 + y**2)
>>> (r, θ)
(5.0,2.214297435588181)

Find a new example of a non-exact calculation result.

>>> 3 ** (logBase 3 10)
10.000000000000002

Why does associativity not apply for the equality, inequality, and comparison operators?

3 < 4 < 5

Because comparison, equality, and inequality operators evaluate to Boolean values which cannot be further operated on with these same operators.