SUMMARY
The discussion focuses on expressing sin(x + π/3) using standard identities, specifically the sine addition formula sin(a + b) = sinAcosB + sinBcosA. The solution provided is sin(x)cos(π/3) + sin(π/3)cos(x), which simplifies to 0.5sin(x) + 0.8660cos(x). It is recommended to express 0.8660 as √3/2 for precision, leading to the final expression of sin(x + π/3) = 0.5sin(x) + (√3/2)cos(x).
PREREQUISITES
- Understanding of trigonometric identities, specifically the sine addition formula.
- Familiarity with the values of trigonometric functions at standard angles, such as π/3.
- Basic algebraic manipulation skills for simplifying expressions.
- Knowledge of exact values versus decimal approximations in trigonometry.
NEXT STEPS
- Study the derivation and applications of the sine addition formula in trigonometry.
- Learn how to convert decimal approximations to exact values in trigonometric functions.
- Explore other trigonometric identities, such as the cosine addition formula.
- Practice simplifying trigonometric expressions using various identities.
USEFUL FOR
Students studying trigonometry, educators teaching trigonometric identities, and anyone looking to enhance their understanding of sine and cosine functions in mathematical expressions.