Transform sine horizontally, stretch and translate together
Interact with the applet to observe how the shape of the graph changes when parameters b and c are changed.[br][br]Observe the coordinates of point A.[br][br]What generalisations can you make about the x coordinate of the point A, relative to the value of b and of c?
Graph 1: y= sin(b(x-c)°)
The values b and c.
Notice that as b increases, the number of complete waves between 0 and 360 changes. [br][br]The horizontal distance between the crest of one wave and the crest of the next wave is called the [url=https://www.mathsisfun.com/algebra/amplitude-period-frequency-phase-shift.html]period[/url].[br][br]Notice that the value c is the horizontal translation or the shift. When we see [math]\text{sin}\left(x-45\right)°[/math] the curve moves 45 units to the right.[br]
1(a)
What is the numerical relationship between the value b in the equation and the period of the curve?
1(b)
What happens to the curve [math]y=\text{sin}\left(x°\right)[/math] when it is transformed to [math]y=\text{sin}\left(x+45\right)°[/math]?
1(c)
The point [math](90,1)[/math] lies on the curve [math]y=\text{sin}\left(x°\right)[/math] . What is the image of this point on the curve [math]y=\text{sin}\left(2\left(x-10\right)°\right)[/math]?
Graph 2.
2(a)
Which one of the following equations is a correct equation for Graph 2?
2 (b)
What is the x coordinate of the point A?
Graph 3.
3(a)
[br]The curve in graph 3 has equation [math]y=\text{sin}\left(b\left(x-c\right)°\right)[/math]. The first local maximum point has x coordinate 85; the second local maximum point has x coordinate 265. [br][br]What is the value of b?
3(b)
The curve in graph 3 has equation [math]y=\text{sin}\left(b\left(x-c\right)°\right)[/math]. The first local maximum point has x coordinate 85; the second local maximum point has x coordinate 265. [br][br]What is the value of c?