To solve the given trigonometric function $\sin(-332^\circ 48')$, we first need to convert the mixed angle of degrees and minutes into a decimal form.

Steps:

1. Convert the minutes (48') into a decimal by dividing by 60: $48' = \frac{48}{60} = 0.8^\circ$

2. Add this to the degrees part: $-332^\circ 48' = -332^\circ + 0.8^\circ = -331.2^\circ$

3. Now, we can find the sine of $-331.2^\circ$ using a calculator or trigonometric function.

Using a calculator:

$\sin(-331.2^\circ) \approx -0.49999999$

So, the decimal approximation of $\sin(-332^\circ 48')$ is approximately:

$\boxed{-0.50000000}$

Let me know if you'd like further clarification or more details! Here are a few related questions for your reference:

1. How do you convert between degrees, minutes, and seconds in trigonometric calculations?
2. What is the effect of a negative angle on the sine function?
3. How can you verify the result of trigonometric functions on a calculator?
4. How would the sine of an angle in the second quadrant differ from one in the fourth quadrant?
5. What are some useful properties of the sine function to remember?

Tip: When dealing with angles that are in minutes or seconds, always convert them into decimal form to simplify calculations.