SUMMARY
The discussion focuses on finding the radian angle θ for the equation cos θ = -1/2 within the interval π ≤ θ ≤ 2π. The first solution identified is θ = 2π/3, which corresponds to the second quadrant. The second angle, located in the third quadrant, can be determined by adding π to the reference angle of 2π/3, resulting in θ = 4π/3. This method effectively utilizes the properties of the unit circle and the cosine function.
PREREQUISITES
- Understanding of trigonometric functions, specifically cosine.
- Familiarity with the unit circle and its quadrants.
- Knowledge of radian measure and angle conversion.
- Basic geometry skills for visualizing angles and their properties.
NEXT STEPS
- Study the unit circle to visualize angles and their corresponding cosine values.
- Learn about the properties of trigonometric functions in different quadrants.
- Explore the concept of reference angles and their applications in trigonometry.
- Practice solving trigonometric equations involving cosine for various intervals.
USEFUL FOR
Students studying trigonometry, educators teaching angle measurement, and anyone seeking to deepen their understanding of the cosine function and its applications in different quadrants.