Video: Finding the Period of Trigonometric Functions

What is the period of ๐‘“(๐‘ฅ) = cos (2๐‘ฅ)?

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Video Transcript

What is the period of ๐‘“ of ๐‘ฅ equals the cos of two ๐‘ฅ?

The general period formula is equal to the regular period of whatever function weโ€™re looking at divided by the absolute value of ๐ต, where ๐ต is the number being multiplied to the variable on the inside of the parentheses. So in this case, ๐ต must be two because two is the number being multiplied to the variable on the inside of the parentheses.

So now we have to know what is the regular period of the cosine function. And the regular period of the cosine function is two ๐œ‹, so we have two ๐œ‹ divided by the absolute value of two. And the absolute value of two is positive two. So two ๐œ‹ divided by two, the twos cancel and we get ๐œ‹.

So when completing these questions, we have to remember that the period goes from one peak to the next or from any point to the next matching point, and this can change between functions.

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