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How To Calculate The Tangent Of An Angle . So called because it can be represented as a line segment tangent to the circle, that is the line that touches the circle, from latin linea tangens or touching line (cf. The tangent of an angle theta, or is the ratio of the opposite leg to the adjacent leg. Tangent Ratio from www.slideshare.net Tan a = sin a / cos a. In the graph above, tan (α) = a/b and tan (β) = b/a. All hope isn't lost, however, because the tangent of an angle θ is defined as sin θ /cos θ.