# Question Video: Finding the Period of Trigonometric Functions Mathematics

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

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### 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. 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 to be two ๐ 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 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 times four, which is eight ๐. And on the denominator, one times three is three.

Therefore, the period of this function would be eight ๐-thirds.