Use this page to explore the effect that each Sine function parameter in the general form of a Sine equation has[br][math]y = a\cdot sin(b(x - h)) + k[/math][br]using the green sliders below.[br][br]Note that the slider value you choose appears in the equation shown at the top right of the graph.

Once you have a sense of the effect each slider has, can you:[br]- Change the period from 2π to π?[br]- Change the amplitude from 1 to 0.5?[br]- Move the entire curve up by 0.5?[br]- Shift the entire curve left by π/2?[br]- How many different ways can you get the curve to pass through the point at (-3π/2, -2)?[br][br]Which parameters worked the way you expected them to, and which did not?[br][br]Of the parameters whose effect surprised you, can you figure out why they did not quite do what you expected them to?[br][br]Note that [b]h[/b] and [b]k[/b] work exactly the way they do with the Point-Slope form of the equation of a line, or the Vertex form of the equation of a parabola: [b]h[/b] is a horizontal translation, and [b]k[/b] is a vertical translation. Why does changing the value of [b]k[/b] cause a vertical translation? [br][br]The constant [b]a[/b] modifies the amplitude of the function. Why does it have this effect?[br][br]Why does changing the value of [b]h[/b] cause a horizontal translation?[br][br]And lastly, and this is a little more subtle, can you figure out and explain why and how [b]b[/b] changes the period of the function the way it does?[br][br]If you wish to use other applets similar to this, you may find an index of all my applets here: [url=https://mathmaine.wordpress.com/2010/04/27/geogebra/]https://mathmaine.com/2010/04/27/geogebra/[/url]