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University of Southern California

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Problem 80

Problem 80

True or False? In Exercises $77-80$ , determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false.

$$\begin{array}{l}{\text { The function } y=3 \cos (x / 3) \text { has a period that is three times }} \\ {\text { that of the function } y=\cos x .}\end{array}$$

Answer

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## Discussion

## Video Transcript

problem Number 80 asks, is determined to determine whether or not the following statement is true or false. The function y equals three Coastline X, divided by three, has a period that is three times that of the function y equals coastline of X. Well, we know that the period of the coast I'm function is equivalent to two pi divided by the absolute value of theme. Now the B in this equation is whatever is being multiplied to our ex inside of the function, so be equals 1/3. So let's see what the period is for this function. Too high, divided by 1/3 positive. So we can drop those absolute value signs and we see that this is the same as three times too high, which equals six pyre. Now, the period of our original function, why equals coastline of X is just won't be equals one, so we can see that that's to fight about it by the to kind of out of it once equals two pie and this is for co sign of X, and this is for three co sign extradited by three, and we can clearly see that's six pi equals three times to find. All right, so let's just do this in red. So it's very clear. Six pi equals three times to five, and so that means this is true.