SUMMARY
The intersection points of cos(x) and sin(x) occur where cos(x) = sin(x). This can be expressed as tan(x) = 1, leading to the solution x = π/4 within the interval 0 < x < π/2. The corresponding y-coordinate at this intersection is y = sin(π/4) = cos(π/4) = √2/2. Therefore, the intersection point is (π/4, √2/2).
PREREQUISITES
- Understanding of trigonometric functions: sine and cosine
- Knowledge of the tangent function and its properties
- Familiarity with solving equations involving trigonometric identities
- Basic concepts of right-angled triangles
NEXT STEPS
- Study the unit circle and its relation to trigonometric functions
- Explore the properties of the tangent function and its graph
- Learn about solving trigonometric equations in different intervals
- Investigate the applications of trigonometric intersections in real-world scenarios
USEFUL FOR
Students of mathematics, educators teaching trigonometry, and anyone interested in understanding the relationships between trigonometric functions.