LearnTronics
A Little Trigonometry — Why Sine?
Why do we call it a sine wave?
The word sine can sound intimidating if trigonometry was a long time ago — or never really clicked in school. We only need a tiny piece of trig to begin.
The school-trig version
For a right triangle:
The symbol θ is the Greek letter theta and commonly stands for an angle.
SOH = Sine = Opposite ÷ Hypotenuse.
You may also hear SOH-CAH-TOA. We only need the SOH part here to understand where the sine relationship comes from.
Another way to think of sine
Imagine a point going around a circle. Watch only how high or low the point is as it rotates. That height rises smoothly, falls through zero, becomes negative, and returns again. Plot that height against time and you get a sine wave.
What is really happening in a generator?
As a conductor or magnetic field rotates, the amount of magnetic flux linked with the winding changes continuously. Under idealized conditions that changing relationship is sinusoidal, so the generated voltage follows a sine wave.
A little history of trigonometry
Trigonometric ideas grew over many centuries from astronomy, surveying, geometry, and navigation. The word and notation evolved through Greek, Indian, Islamic, and European mathematics. Electrical engineers later found sine and cosine especially convenient for describing rotating machines and periodic signals.
Worked idea — no calculator
At 0°, sine is 0. At 90°, sine is 1. At 180°, it is back to 0. At 270°, it is −1. At 360°, it returns to 0 and the cycle starts again.
Try these yourself
A little deeper
A sinusoidal voltage can be written:
ω (omega) is angular frequency. Later we will connect it to ordinary frequency with ω = 2πf. For now, recognize the expression as “peak voltage times a repeating sine-wave shape.”