A periodic sequence is defined by $U_n = ext{sin}igg(rac{n ext{π}}{2}igg)$ State the period of this sequence - AQA - A-Level Maths Pure - Question 3 - 2018 - Paper 1

The period of the sine function is generally $2π$. However, since the argument of the sine function here is rac{n ext{π}}{2}, we need to determine how this affects the period.

To find the period, we set the argument equal for subsequent cycles:

rac{(n + T) ext{π}}{2} = rac{n ext{π}}{2} + 2π

This simplifies to:

$T ext{π} = 4π$ $T = 4$

Thus, the period of the sequence is 4.