Final answer:
The error in approximating sin(x) using the small angle approximation is given by the difference between the actual value and the approximate value.
Step-by-step explanation:
The error in approximating sin(x) using the small angle approximation can be calculated by finding the difference between the actual value of sin(x) and the approximate value. The small angle approximation assumes that for small angles, sin(x) is approximately equal to x. So the error is given by:
error = |actual value - approximate value| = |sin(x) - x|
For example, if x = 0.1 radians, the actual value of sin(x) is approximately 0.0998334166, while the approximate value using the small angle approximation is 0.1. So the error would be |0.0998334166 - 0.1| = 0.0001665834.