Sinusoidal waveform properties: A single sine wave (steady-state AC) can be described as having which of the following features?

Introduction:
Sine waves are fundamental to AC analysis and Fourier methods. Several equivalent descriptors apply depending on whether we look at the waveform in time, sign, or coordinate representation. This question asks you to recognize that multiple statements about a standard sine wave can simultaneously be true.

Given Data / Assumptions:

• Ideal sinusoid with constant amplitude and frequency.
• Observation over one complete cycle.
• Standard mathematical definitions of period and quadrants.

Concept / Approach:
Over one cycle, the sine wave completes one period. It also has two alternations: a positive half-cycle and a negative half-cycle. In the angle (phasor) domain, we often reference four quadrants corresponding to 0–90°, 90–180°, 180–270°, and 270–360°, across which sine changes sign and magnitude systematically.

Step-by-Step Solution:

Verification / Alternative check:
Plot sin(θ) from 0° to 360° and note sign/magnitude behavior per quadrant; in the time domain, count zero crossings and extrema to verify two alternations within one period.

Why Other Options Are Wrong:

• Each individual statement is correct, but the most complete answer acknowledging all is “all of the above.”

Common Pitfalls:
Assuming these descriptions are mutually exclusive; conflating “quadrants” (angle domain) with “alternations” (time domain).

Final Answer:
all of the above