Transforming sine and cosine curves

1
Transforming sine and cosine curves

• www.ibmaths.com

2
Learning outcomes. You will be able to
understand the terms amplitude, period, and shift.
For the purpose of this tutorial all the graphs
are in degrees and the domain of x is from 0 to
360 degrees.
3
Amplitude of a trig graph
A graph of ysin(x) is shown below.
This graph has an amplitude of 1.
The graph of y2sin(x) has an amplitude of 2.
The graph of y3sin(x) has an amplitude of 3.
This pattern will also work with cosine graphs.
4
Period of a trig graph
A graph of ycos(x) is shown below.
This graph has an period of 360 - the length it
takes to make a complete wave.
The graph of ycos(2x) has an period of 180.
The graph of ycos(3x) has an period of 120.
Can you see the pattern?
This pattern will also work with sine graphs.
5
Shift of a trig graph
A graph of ycos(x) is shown below.
Look at where this graph starts (0,1).
The graph of ycos(x)2 has a shift of 2.
The graph of ycos(x)-3 has a shift of -3
This pattern will also work with sine graphs.
6
How much did you understand?
Write down the amplitude of each of these
equations.
1. y2sinx 2. y0.5cosx 3.y5sinx
1. amplitude 2 2. amplitude 0.5 3.
amplitude 5
Write down the period of each of these equations.
4. ysin(4x) 5. ycos(0.5x) 6.ysin(3x)
4. period 90 degrees 5. period 720
degrees 6. period 120 degrees
Click for answers
7
How much did you understand?
The graph shows yacos(bx)c. Find the values of
a, b and c. Hint use your GDC
a2, b3, c-1
The graph shows yasin(bx)c. Find the values of
a, b and c. Hint use your GDC
a3, b0.5, c-2