SUMMARY
The graph of the function \( y = \sin^2 x + \cos^2 x \) is indeed a constant value of \( y = 1 \) for all values of \( x \). This conclusion is derived from the Pythagorean identity, which states that the sum of the squares of the sine and cosine of an angle equals one. Therefore, the graph is a horizontal line at \( y = 1 \), confirming that the initial assumption was correct.
PREREQUISITES
- Understanding of trigonometric functions, specifically sine and cosine.
- Familiarity with the Pythagorean identity in trigonometry.
- Basic knowledge of graphing functions in Cartesian coordinates.
- Ability to interpret mathematical notation and equations.
NEXT STEPS
- Study the Pythagorean identity in detail and its applications in trigonometry.
- Learn how to graph trigonometric functions and their transformations.
- Explore other trigonometric identities and their proofs.
- Investigate the implications of constant functions in calculus and their derivatives.
USEFUL FOR
Students of mathematics, educators teaching trigonometry, and anyone interested in understanding the properties of trigonometric functions and their graphs.