SUMMARY
The discussion focuses on graphing cosine and sine functions, specifically addressing the equations for two problems. For problem #3, the correct equation is identified as y=3cos(π/2)(x-2), with an amplitude of 3 and a horizontal shift of 2 units to the right. In problem #4, the amplitude is 2, with a left shift of 1 unit and an upward shift of 3 units. The participants confirm the correctness of these equations but suggest simplifying the first equation using the identity cos(x - π) = -cos(x).
PREREQUISITES
- Understanding of trigonometric functions and their properties
- Knowledge of amplitude, phase shifts, and vertical shifts in graphing
- Familiarity with cosine function identities
- Basic algebra skills for manipulating equations
NEXT STEPS
- Study the properties of trigonometric functions in detail
- Learn about phase shifts and how they affect graphing
- Explore trigonometric identities, particularly those involving cosine
- Practice graphing various trigonometric functions with different transformations
USEFUL FOR
Students studying trigonometry, educators teaching graphing techniques, and anyone looking to improve their understanding of trigonometric functions and their transformations.