When identifying a sinusoidal function, you may use the basic shape of either the sine curve or the cosine curve – one is just a horizontal transformation of the other!
The curve in the figure above can take the equation or .
Use the applet to view the four basic shapes.
It has been noted above that . In other words, if you slide the cosine function 90 units to the right, your curve can be expressed as the sine function.
In a similar way, complete:
- (Move the cosine curve 90 units left, you may do this on the applet just reset it when done to avoid confusion.)
When a curve takes one of these four basic shapes shown in the applet, we can avoid using a horizontal transformation.
Reproduce the following graphs on geogebra; using only functions of the form or (that is, no horizontal translation).