Cosecant, Secant, and Cotangent
In addition to sine, cosine, and tangent, there are three
other trigonometric functions you need to know for the Math IIC:
cosecant, secant, and cotangent. These functions are simply the
reciprocals of sine, cosine, and tangent.
Cosecant is the reciprocal of sine. Its formula is:
Secant is the reciprocal of cosine. Its formula is:
Cotangent is the reciprocal of tangent. Its formula is:
The Math IIC will rarely ask you to find the values of
these three functions. Most likely, it will ask you to manipulate
them in algebraic equations, often with the goal of simplifying the
expression down to its simplest form. For example:
We can simplify the expression by eliminating the secants
and cosecants because we know that they are simply the reciprocals
of cosine and sine, respectively. We will also make use of the trigonometric
Plug tan 45º into your calculator, and you get the nice,
clean number 1 as an answer.
It’s also possible you might have to deal with cosecant,
secant, and cotangent in questions that cover trigonometric identities
(we’ll cover the important identities later in this chapter).