Sine and cosine are not the only trigonometric functions used in trigonometry. Many others have been used throughout the ages, things like haversines and spreads. The most useful of these is the tangent. In terms of the unit circle diagram, the tangent is the length of the vertical line ED tangent to the circle from the point of tangency E to the point D where that tangent line cuts the ray AD forming the angle.
Drag the point B around to see how the sine, cosine, and tangent change as you change the angle.
Tangent in terms of sine and cosine
Since the two triangles ADE and ABC are similar, we have
ED / AE = CB / AC.
But ED = tan A, AE = 1, CB = sin A, and AC = cos AB. Therefore we have derived the fundamental identity:-
tanA=sinA/cosA.
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