Overview
This lesson introduces the basic sine (sin) graph, its key features, and important related terms for grade 10 trigonometry.
The Basic Sine Graph
- The sine graph uses x-values measured in degrees (e.g., 0°, 90°, 180°, 270°, 360°).
- The y-axis typically ranges from -1 to 1, sometimes extending to -2 or 2 depending on scaling.
- Key points: sin(0°) = 0, sin(90°) = 1, sin(180°) = 0, sin(270°) = -1, sin(360°) = 0.
- The basic sine graph forms a continuous wave pattern that repeats every 360°.
- The graph can be extended forward and backward beyond -360° and 360°.
Drawing and Understanding the Sine Graph
- Plot points using a calculator for sin values at standard angles.
- Connect points smoothly to create the wave, not with straight lines.
- The standard sine graph equation is y = sin x.
- Changing the equation (like y = 2 sin x or y = sin x + 2) alters the wave's amplitude or vertical position but keeps the wave shape.
Key Concepts: Period, Domain, Range, Amplitude
- Period: The horizontal length before the graph repeats; always 360° for grade 10.
- Domain: Describes all possible x-values; usually set by the question, e.g., –360° ≤ x ≤ 360°.
- Range: Describes all possible y-values; for the basic sine graph, –1 ≤ y ≤ 1.
- Amplitude: The distance from the halfway (resting) position (y = 0) to the highest point (y = 1); amplitude is 1 for y = sin x.
Key Terms & Definitions
- Sine Graph (Sin Graph) — The graph of the function y = sin x, forming a repeating wave.
- Period — The interval after which the graph repeats, 360° for basic sine.
- Domain — The set of x-values shown or allowed on the graph.
- Range — The set of y-values the graph takes.
- Amplitude — The maximum height from the midpoint (resting position) to a peak.
Action Items / Next Steps
- Practice plotting basic sine graphs using a calculator for sin values at standard angles.
- Memorize the period (360°), amplitude (1), domain, and range for the basic sine graph.
- Prepare for upcoming lessons on cosine and tangent graphs.