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:
is the reciprocal of sine. The reciprocal of a number a is 1/a, so
you see that
In other words, cosecant is the ratio of the hypotenuse to the opposite leg.
is the reciprocal of cosine:
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.
is the reciprocal of tangent. (How's that for obvious?) You have the hang of this if you've looked at the previous bullets:
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.