Sine and cosine are the two most fundamental trigonometric functions. Both are periodic waves with the same shape — but they start at different points. Understanding their differences is key to mastering trigonometry.
The Key Difference: Starting Point
Sine starts at 0: sin(0) = 0. The curve rises to its maximum of 1 at x = π/2. Cosine starts at its maximum: cos(0) = 1. The curve falls to 0 at x = π/2. In other words, cosine is just sine shifted left by π/2.
Amplitude, Period, and Phase Shift
Both functions follow the general form f(x) = A·sin(Bx + C) + D (or cosine). A controls amplitude (height), B controls period (2π/B), C controls phase shift (horizontal shift), and D controls vertical shift.
When to Use Sine vs Cosine
Use sine when modeling phenomena that start at zero (like a pendulum starting from rest). Use cosine when modeling phenomena that start at maximum (like a spring at maximum compression). In practice, either can model any wave — they are just shifted versions of each other.