# Sine transformation

1. y = a sin(x)  Vertical Stretch

Use the slider given in the top left and change the values of ‘a’ to see the transformation Changing values of ‘a’ affects the amplitude of the “Sine” function.

The amplitude is |a|.

By changing the values of a in y = a sin(x) the curve getting stretch along y axis and the stretch factor is ‘a’ units

There is no change in the period or x intercepts of the curve.

The value of a can be found using the maximum and minimum values of the curve.

2. y = sin(b x)  Horizontal stretch

Use the slider given in the top left to change the values of ‘b’ to see the transformation.

Changing the value of b affects the period of the “Sine” curve.

The period is 2pi / b.

By changing the values of b in y = sin(bx) the curve getting stretch along x axis and stretch factor is “1/a”

There is no change in the amplitude of the curve.

The value of a can be found observing the period of the curve,

b = 2pi/ period

3. y = sin(x-c)  Horizontal translation

Use the slider given in the top left and change the values of ‘c’ to see the transformation. Changing values of ‘c’ affects the horizontal translation of the

“Sine” function.

By changing the values of ‘c’ in y = sin(x-c) the curve getting horizontal sift. If c is positive the curve moves towards right and if ‘c’ value is negative the curve moves ‘c’ units towards left.

There is no change in the period , amplitude and the vertical shift.

4. y = sin(x) +d  Vertical translation

Use the slider given in the top left and change the values of ‘d’ to see the transformation Changing values of ‘d’ affects the vertical movement of the “Sine” function.

By changing the values of d in y = sin(x) +d the curve getting translation along y axis and it moves  ‘d’ units

There is no change in the period or x intercepts of the curve.

The value of a can be found using the maximum and minimum values of the curve

5. Combine Transformation y = a sin[b(x-c)] +d  Vertical translation

Skill builder questions

 Practice worksheet – 1 Angle of any magnitude Practice worksheet – 2 Convert degree – radian Practice worksheet – 3 Measure angle worksheet