Question Video: Finding the Period of Trigonometric Functions Mathematics

What is the period of ๐‘“(๐‘ฅ) = (2/3) cos (3๐‘ฅ/4)?


Video Transcript

What is the period of ๐‘“ of ๐‘ฅ equals two-thirds cosine of three-fourths ๐‘ฅ?

The general period formula is equal to the regular period of the function, so whatever the function is and in this case itโ€™s cosine, divided by the absolute value of ๐ต. And ๐ต is the constant that is being multiplied to the variable on the inside of that parenthesis. So here, ๐ต would be the three-fourths thatโ€™s being multiplied to the ๐‘ฅ on the inside of that function. So what is the regular period of the cosine function? That is two ๐œ‹. And then as we said, ๐ต is equal to three-fourths. And itโ€™s the absolute value of three-fourths, which is three-fourths because the absolute value sign makes anything positive. So since itโ€™s a positive three-fourths, it stays at three-fourths.

So we can go ahead and take what we have but change two ๐œ‹ to be two ๐œ‹ over one. So here we are dividing fractions. And when you divide fractions, we end up multiplying by the denominatorโ€™s reciprocal. So we take our top fraction on the numerator, two ๐œ‹ divided by one, and instead of dividing by three-fourths, we are multiplying by the reciprocal of three-fourths. So weโ€™re actually multiplying by four-thirds. So we take two ๐œ‹ times four, which is eight ๐œ‹. And on the denominator, one times three is three.

Therefore, the period of this function would be eight ๐œ‹-thirds.

Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.