The unit circle and trig functions
The unit circle is a circle of radius 1 centered at the origin. For any angle θ measured from the positive x-axis, the terminal point on the circle has coordinates (cos θ, sin θ).
The other four trig functions are derived from sine and cosine: tan θ = sin θ / cos θ, cot θ = cos θ / sin θ, sec θ = 1 / cos θ, csc θ = 1 / sin θ. Some of these are undefined at certain angles (e.g., tan 90° is undefined because cos 90° = 0).
(x, y) = (cos θ, sin θ)
Coordinates on the unit circle.
tan θ = sin θ / cos θ
Tangent as a ratio of sine to cosine.