Given a point, P(x, y), on the unit circle we can create a triangle by drawing the straight lines from the point to the x-axis and from P to the origin. This creates a triangle with vertices P, (x, 0), and (0, 0). This also creates an angle starting at the x-axis and ending at the line segment from P to the origin. This allows us to define the six trigonometric(trig) functions based on the cordinates of P. All of the trigonometric functions take the angle created by the mentioned line segment, when defined.
The sine function outputs the y coordinate of P.
The cosine function outputs the x coordinate of P.
The tangent function outputs the ratio of the x-ccordinate of P to the y-coordinate of P, so
The cosecant function outputes the reciprocal of the sine function output, when defined. So when y is nonzero, the cosecant function outputs
The secant function outputs the reciprocal of the cosine functions output, when defined.
The cotangent function outputs the reciprocal of the tangent functions output, when defined.