If the instructions for a problem ask you to use the smallest possible domain to completely graph two periods of y = 5 + 3 cos 2(x -pi/3), what should be used for Xmin and Xmax? Explain your answer.

Question

anonymous · Answer

The period of cos(x) is -pi<x<pi. The given function,  $$3\cos(2x- 2\pi/3) $$ oscillates twice as fast as cos(x)- use a graphing calculator to confirm. Therefore, the period is half as long. Therefore, a full period is graphed on $$-0.5\pi \le x \le 0.5\pi$$ or $$0 \le x \le \pi$$This domain graphs ONE period of the cos function, centered about 0. [The period of cos(2*x) is pi, think about unit circle]. Therefore, two periods are 2pi, or $$-\pi \le x \le \pi$$. However, your teacher may be asking for the domain starting at 0, rather than centered about it. In this case the domain may be expressed as $$0 \le x \le 2\pi $$ 
Therefore;
$$XMIN=0$$
and

$$XMAX=2\pi$$
Hope that helps.