Final answer:
The Maclaurin series for sin(x) is used for approximating the value of the sine function, but the angle is missing in the question. Examples of rounding to a certain number of significant figures are given, ranging from two to five significant figures.
Step-by-step explanation:
The original question seems to be incomplete, as it asks to use the first five terms of the trigonometric series to approximate the value of sin, but it does not provide the angle for which to approximate the sine value. However, for educational purposes, we can discuss the sine approximation using the Maclaurin series for sine (which is a special case of Taylor series at x=0).
The Maclaurin series for sin(x) is:
sin(x) = x - (x^3/3!) + (x^5/5!) - (x^7/7!) + (x^9/9!) - ...
To approximate sin(x) using the first five terms of the series, we would plug the value of x into:
sin(x) ≈ x - (x^3/6) + (x^5/120) - (x^7/5040) + (x^9/362880)
Without a given x value, the answer cannot be determined from the options provided (A. 0.0074, B. 0.0697, C. 0.0747, D. 0.0069). The question needs to specify the angle in radians for which the sine value is to be approximated.
As for significant figures, here are examples of rounding:
- (a) 0.424 (rounded to two significant figures) becomes 0.42
- (b) 0.0038661 (rounded to three significant figures) becomes 0.00387
- (c) 421.25 (rounded to four significant figures) becomes 421.3
- (d) 28,683.5 (rounded to five significant figures) becomes 28,684