Approximate $\sin 0.3$ to four decimal places using the third-degree Maclaurin polynomial for $f\left(x\right)=\sin x$.

• A. $0.0045$
• B. $0.3000$
• C. $0.2955$
• D. $0.3045$

Answer: (C)

Verified step by step guidance

1. Step 1: Recall the Maclaurin series expansion for f(x) = sin(x). The general formula is: sin(x) ≈ x - (x³/3!) + (x⁵/5!) - ... . For a third-degree polynomial, we only consider terms up to x³.
2. Step 2: Substitute x = 0.3 into the truncated Maclaurin series: sin(0.3) ≈ 0.3 - (0.3³/3!).
3. Step 3: Compute the factorial in the denominator of the second term. Note that 3! = 3 × 2 × 1 = 6.
4. Step 4: Simplify the expression by calculating 0.3³ and dividing it by 6. Combine this result with the first term (0.3).
5. Step 5: The resulting value is the approximation of sin(0.3) using the third-degree Maclaurin polynomial. Round the result to four decimal places.