Trig Functions and Plane Transformations

Explore the plane transformations applied to the sine and cosine functions. How does the function graph modify if we apply some "classic" transformations (horizontal and vertical translations, dilations, composition with function, etc) ? Before viewing the resulting graph, try to determine the new position of some "convenient" points related to the transformed function (e.g. the intersections with the x and y axes), as well as the possible variations of the main characteristics of the function (amplitude, period...). Move the sliders to explore dynamically the magnitudes of translations and dilations, and drag point P along the graph of the parent function to view the graph of the transformed one. Deselect the Instructions checkbox to start exploring transformations. A button displayed on bottom right of the app allows you to delete traces.