Trigonometry got its start in Sumerian astronomy with the division of the circle into 360 degrees, and with the study of similar triangles, but did not become systematic until Hipparcos. The three principal trig functions are defined as in this diagram.
In this diagram based on a unit circle the tangent function of the given angle is the length of a tangent (Latin tangere, touch) to the circle, and the secant is the length of a secant (Latin, secare, cut) from the center of the circle, cutting the circle and extending to the end of the tangent. The measure of the angle is the length of the circular arc. This is known as radian measure.