Question Video: Calculating the Period of a Trigonometric Function Mathematics • First Year of Secondary School

Video Transcript

Find the period of the function 𝑓 of 𝑥 is equal to sin three 𝑥.

We will begin by considering the sine function and its properties, namely, its period. The sine function is periodic, with a period of two 𝜋 radians or 360 degrees. Next, we recall that for any function sin 𝑛𝑥, the period of the function will be equal to two 𝜋 over 𝑛. In this question, our function 𝑓 of 𝑥 is equal to sin three 𝑥. This means that 𝑛 is equal to three, and as such the period of the function is two 𝜋 over three.

We can therefore conclude that the period of the function 𝑓 of 𝑥 is equal to sin three 𝑥 is two 𝜋 over three. Whilst it is not required in this question, the graph of the function 𝑓 of 𝑥 is equal to sin three 𝑥 is as shown.