Use what you know about the transformation of functions from [math]f\left(x\right)[/math] to [math]af\left(x\right)[/math] to predict the shape of the graph sine and cosine.
The following is graph of [math]f\left(x\right)=sin\left(x\right)[/math] and [math]g\left(x\right)=a\cdot sin\left(x\right)[/math].[br]Move the slider [math]a[/math] and identify what changes in the graph.
a) [math]y=2\cdot sin\left(x\right)[/math][br][br]b) [math]y=\frac{1}{2}\cdot sin\left(x\right)[/math][br][br]c) [math]y=a\cdot sin\left(x\right)[/math]
The following is graph of [math]f\left(x\right)=cos\left(x\right)[/math] and [math]g\left(x\right)=a\cdot cos\left(x\right)[/math].[br]Move the slider [math]a[/math] and identify what changes in the graph.
a) [math]y=2\cdot cos\left(x\right)[/math][br][br]b) [math]y=\frac{1}{2}\cdot cos\left(x\right)[/math][br][br]c) [math]y=a\cdot cos\left(x\right)[/math]
Make a generalization of the effect of parameter "[math]a[/math]" on the graph of [math]y=a.sin\left(x\right)[/math] and [math]y=a.cos\left(x\right)[/math].