The Basic Sine and Cosine Curves

Trigonometry · Axiom Academy

LESSON The Basic Sine and Cosine Curves A detailed exploration of y = sin(x) and y = cos(x), the fundamental periodic functions that describe wave patterns, circular motion, and oscillations. The sine and cosine functions create smooth, repeating wave patterns. While they have the same shape, they're shifted relative to each other: 2. Amplitude: Height of the Wave The amplitude is the maximum distance from the center line to the peak (or trough) of the wave. For both y = sin(x) and y = cos(x), the amplitude is 1. 3. Period: Length of One Complete Cycle The period is the horizontal distance required for the function to complete one full cycle before repeating. Both sine and cosine have a period of 2π. 4. Key Points: Intercepts and Extrema Understanding the intercepts (where the curve crosses the x-axis) and extrema (maximum and minimum points) is crucial for analyzing these functions. 5. The Relationship Between Sine and Cosine Sine and cosine are intimately related: cosine is simply sine shifted left by π/2 (or 90°). This relationship is fundamental to many trigonometric identities. Domain: All real numbers (-∞, ∞) Continuous and smooth everywhere Odd function (sine) vs Even function (cosine)

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