Identify the end of a sample period for the function:

Question

 

a. x=3pi/2

b. x=7pi/4

c. x=9pi/4

d. x=5pi/4

Answer 1

For a standard sine or cosine function, the period is 2π, meaning the function repeats itself every 2π units. The “sample period” refers to one full cycle of the function. If we start at x=0, the first complete cycle ends at x=2π.

Looking at the options:

1. x=3π/2=→ 1.5π, this is not a full cycle.
2. x=7π/4→ 1.75π, this is not a full cycle.
3. x=9π/4 → 2.25π, just past one full cycle.
4. x=5π/4 → 1.25π, this is not a full cycle.

So, the end of the first sample period would be closest to x=9π/4 ​.