Cosecant, Secant, and Cotangent
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
Cosecant is the reciprocal of sine. Its formula is:
Secant
Secant is the reciprocal of cosine. Its formula is:
Cotangent
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:
What is , if = ?
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 identity tan = :
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).
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