The Unit Circle & Origins
Angle (θ)
Terminal Arm
Sine
Cosine
Why the strange names?
- Sine: From Sanskrit jya (chord). Translated to Arabic as jiba. European translators mistook it for jaib (bay/fold) and used the Latin equivalent sinus.
- Cosine: Short for Latin complementi sinus. It is literally the "sine of the complementary angle".
- Tangent: From Latin tangere ("to touch"). The line segment touches the unit circle at a single point (x=1).
Visualizing the Ratios
On a circle with radius :
- Terminal Arm is the main radius line set at the angle.
- Cosine is the x-coordinate.
- Sine is the y-coordinate.
- Tangent (Green line) is the y-coordinate where the extended line hits the vertical tangent boundary at right.