Graphs of Sine and Cosine 1.2 An applet illustrating how the graphs of sine and cosine are related to the unit circle. Transformations of Functions 1.3 An applet illustrating how transformations ...

That function, for example ... Huh, Katz and Adiprasito spent four years searching for the right way to translate certain ideas into the realm of graphs. Once they’d found it, a proof of the Rota ...

Writing graphs as functions in the form \(f(x)\) is useful when applying translations and reflections to graphs. If \(f(x) = x^2\), then \(f(x) + a = x^2 + a\). Here we are adding \(a\) to the ...

Graphically, \(f(x) = x^2\) is the same as the graph of \(y = x^2\). Writing graphs as functions in the form of \(f(x)\) is useful when applying translations and reflections to graphs.

Students are taught the "unit circle" and its relationship to trigonometry, but many fail to make the leap on how crucial circles are for trig functions. With static graphs and equations ...