Sketch one complete period of a cosine graph with the follow

Sketch one complete period of a cosine graph with the following transformations. Remember to label your axes carefully (with appropriate numbers) and to show the five points accurately. Period: 20 Phase shift: 5 left Amplitude: 2 x-axis reflection No shift up/down Write an equation that represents the curve described above.

Solution

The equation is of the form y=Acos(BX-C)

And in the given question, A=2

period,2pi/B=20

B=pi/10

Phase shift ,C/B=-5

C=-pi/2

So the required equation is y=-2cos(pi x/10 +pi/2)