Translation (sliding a curve, usually along an axis)
Now that you know what the graphs start out like, lets now look at what graphs would look like of the form:
\(y = a\sin bx + c\)
where:
- a = amplitude (half the length from the maximum to the minimum values)
- b = how many waves between 0˚ and 360˚
- c = by how much has the graph been moved up (c > 0) or down (c < 0)
Examples of sketching graphs
1) Sketch the graph of \(y = 5\sin 2x^\circ + 4\)
- amplitude = 5, so the distance between the maximum and minimum value is 10
- number of waves = 2 (Each wave has a period of 360˚ ÷ 2 = 180˚)
- moved up by 4 (since c > 0)
- maximum turning point when \((5\times 1)+4=9\) and minimum turning point when \((5\times{-1})+4=-1\) (This is because the maximum of sine is 1 whether it is sinx or sin2x . and the minimum of sine is -1)
The graph looks like:
2) Sketching the graph of \(y = 3\cos \frac{1}{2}x^\circ - 1\)
- amplitude = 3, so the distance between the maximum and minimum value is 6
- number of waves = 0.5 (Each wave has a period of 360˚ ÷ 0.5 = 720˚)
- moved down by 1 (since c < 0)
- maximum turning point when \(y=(3\times 1)-1=2\) and minimum turning point when \(y=(3\times 1)-1=-4\)