The reciprocal identities define three trigonometric functions: cosecant, secant and cotangent in terms of the primary trigonometric functions: sine, cosine and tangent. The most commonly used reciprocal function is cotangent, the other two are mostly included for historical purposes.
The geometry of the reciprocal identities can be visualized on the unit circle by drawing the line tangent to the point formed by the angle. This line intersects the axes forming a right triangle whose base is equal to secant and height is equal to cosecant.
The secant of an angle is the reciprocal of the cosine of the same angle. This can be seen visually by graphing the two functions. As cosine approaches 1, secant approaches 1 and as cosine approaches 0, secant diverges to infinity.
The cosecant of an angle is the reciprocal of the sine of the same angle. This can be seen visually by graphing the two functions. As sine approaches 1, sine approaches 1 and as sine approaches 0, cosecant diverges to infinity.
The cotangent of an angle is the reciprocal of the tangent of the same angle. This can be seen visually by graphing the two functions. As tangent approaches 1, cotangent approaches 1 and as tangent approaches 0, cotangent diverges to infinity.
