SUMMARY
To find Cos2A given that sinA = -1/3 and the interval π ≤ A ≤ 3π/2, utilize the identity cos(2A) = 1 - sin²(A). First, calculate sin²(A) which equals (1/3)² = 1/9. Then, substitute this value into the identity to find cos(2A) = 1 - 1/9 = 8/9. The solution confirms that the approach using trigonometric identities is efficient for this problem.
PREREQUISITES
- Understanding of trigonometric identities, specifically cos(2A) and sin²(A).
- Knowledge of the unit circle and the behavior of sine and cosine functions within specified intervals.
- Ability to perform basic algebraic manipulations and substitutions.
- Familiarity with the concept of inverse trigonometric functions, particularly sin⁻¹.
NEXT STEPS
- Study the derivation and applications of trigonometric identities, focusing on double angle formulas.
- Explore the unit circle to better understand the sine and cosine values in different quadrants.
- Practice solving trigonometric equations within specified intervals to enhance problem-solving skills.
- Learn about the implications of sine and cosine values in real-world applications, such as wave functions.
USEFUL FOR
Students studying trigonometry, mathematics educators, and anyone looking to strengthen their understanding of trigonometric identities and equations.