To determine the minimum number of points required to mark all maximum, minimum, and zeros in one period of a sinusoid, let's analyze the properties of a standard sinusoidal function, [tex]\( y = A \sin(Bx + C) + D \)[/tex]:
1. Maximum Point: In one period of the sinusoid, there is one point where the function reaches its maximum value.
2. Minimum Point: Similarly, in one period, there is one point where the function reaches its minimum value.
3. Zero Crossing Points: There are two points in one period where the sinusoid crosses the horizontal axis (y = 0).
A complete period of a sinusoid thus includes:
- 1 maximum point
- 1 minimum point
- 2 zero crossing points
Adding these together, we get:
[tex]\[
\text{Total points} = 1 \text{ (maximum point)} + 1 \text{ (minimum point)} + 2 \text{ (zero points)} = 4 \text{ points}
\][/tex]
Therefore, the minimum number of points required to mark all maximum, minimum, and zeros in one period of a sinusoid is 4.
Answer: 4 points
