SUMMARY
The correct Taylor expansion for sin x around -π/4 to the fourth term is given by the formula: sin(-π/4) + cos(-π/4)(x + π/4) - 0.5sin(-π/4)(x + π/4)² - (1/6)cos(-π/4)(x + π/4)³. Evaluating sin(-π/4) and cos(-π/4) yields -√2/2 and √2/2, respectively. The mistake in the initial calculation likely stems from incorrect application of the Taylor series formula or miscalculation of the coefficients.
PREREQUISITES
- Understanding of Taylor series expansion
- Knowledge of trigonometric functions and their derivatives
- Familiarity with evaluating limits and series
- Basic algebraic manipulation skills
NEXT STEPS
- Study the derivation of Taylor series for trigonometric functions
- Practice calculating higher-order derivatives of sin x
- Learn about error analysis in Taylor series approximations
- Explore applications of Taylor series in physics and engineering
USEFUL FOR
Students and educators in mathematics, particularly those focusing on calculus and series expansions, as well as anyone needing to apply Taylor series in practical scenarios.