# Transform sine horizontally, stretch and translate together

- Author:
- Lee W Fisher

- Topic:
- Functions, Sine, Geometric Transformations

Interact with the applet to observe how the shape of the graph changes when parameters b and c are changed.
Observe the coordinates of point A.
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.
The horizontal distance between the crest of one wave and the crest of the next wave is called the period.
Notice that the value c is the horizontal translation or the shift. When we see the curve moves 45 units to the right.

## 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 when it is transformed to ?

## 1(c)

The point lies on the curve . What is the image of this point on the curve ?

## 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)

The curve in graph 3 has equation . The first local maximum point has x coordinate 85; the second local maximum point has x coordinate 265. What is the value of b?

## 3(b)

The curve in graph 3 has equation . The first local maximum point has x coordinate 85; the second local maximum point has x coordinate 265. What is the value of c?