Picture a wave that starts at zero, rises to a peak of 1 at x = π/2 (about 1.57), falls back through zero at π, dips to a trough of -1 at 3π/2 (about 4.71), and returns to zero at 2π. It's a smooth, repeating curve that crosses the x-axis at 0, π and 2π.
For the quiz, a few things to memorize from that shape:
- Key points: (0, 0), (π/2, 1), (π, 0), (3π/2, -1), (2π, 0). Plotting those five points and sketching a smooth curve through them gets you most of the graph.
- Period: one full cycle takes 2π, so the pattern repeats after that.
- Symmetry: sin(x) is odd, meaning sin(-x) = -sin(x), so it's symmetric about the origin.
If you want to check your sketch against a labeled graph, search for "sine wave unit circle graph" in an image search or a Khan Academy trig lesson, which pairs the unit circle with the curve. Good luck on the quiz.
🔎 Wikimedia Commons: sine wave graph
