Trigonometric ratios are defined using the unit circle: for angle theta, sin(theta) and cos(theta) are the y and x coordinates of the corresponding point on the unit circle. The remaining four ratios — tan, cot, sec, csc — are derived from sin and cos. The ASTC rule determines signs across the four quadrants: All ratios positive in Q1, only Sin in Q2, only Tan in Q3, only Cos in Q4. Standard angles (0, 30, 45, 60, 90 degrees) have exact values that must be memorized. Allied angle formulas reduce any angle to the first quadrant using the rule: for (n*pi/2 +/- theta), the function changes to its co-function when n is odd and retains its name when n is even, with the sign determined by the ASTC rule applied to the original function in the relevant quadrant.