SUMMARY
The original equation y=-3sin(2x) is transformed by shifting it 30 degrees to the left and 5 units up, resulting in the new equation y=-3sin[2(x+30)]+5. The correct application of the transformation formula y=Asin(k(x-c))+b indicates that a negative value for c results in a leftward shift. The incorrect formulation y=-3sin[2(x-30)]+5 was identified as shifting the function to the right instead.
PREREQUISITES
- Understanding of trigonometric functions and transformations
- Familiarity with the sine function and its properties
- Knowledge of the transformation formula y=Asin(k(x-c))+b
- Experience with graphing tools like Graphmatica
NEXT STEPS
- Study the properties of sine functions and their transformations
- Learn how to apply the transformation formula y=Asin(k(x-c))+b in various scenarios
- Explore graphing techniques using Graphmatica for visualizing transformations
- Investigate common mistakes in function transformations to avoid errors
USEFUL FOR
Students and educators in mathematics, particularly those focusing on trigonometry and function transformations, as well as anyone using graphing software for visual analysis.