# How to Calculate an Angle Using Reciprocal Trigonometric Functions

Three trigonometric ratios — secant, cosecant, and cotangent — are called *reciprocal functions* because they're the reciprocals of sine, cosine, and tangent. These three functions open up three more ways in which you can solve equations in pre-calculus. The following list breaks down these functions and how you use them:

*Cosecant*, orThe reciprocal of a number*a*is*1/a*, soBecause

you see that

In other words, cosecant is the ratio of the hypotenuse to the opposite leg.

*Secant*, or:Secant, in other words, is the ratio of the hypotenuse to the adjacent leg.

A common mistake is to think that secant is the reciprocal of sine and that cosecant is the reciprocal of cosine, but the previous bullets illustrate the truth.

*Cotangent*, or**is the reciprocal of tangent.**(How's that for obvious?) You have the hang of this if you've looked at the previous bullets:Therefore,

Remember that secant, cosecant, and cotangent are all reciprocals, but you typically won't find a button for them on your calculator. You must use their reciprocals — sine, cosine, and tangent. Don't get confused and use the sin

^{–1}, cos^{–1}, and tan^{–1}buttons, either. Those buttons are for the inverse trig functions.