# Real World Example for Cosecant or Secant

Cantor
I am math teacher and was asked the classic question, "Where am I ever going to use this in life" I usually have a real word example, but for the cosecant function I am stuck (Besides higher level math classes.) Anyone know a specific example?

Russell Berty
I also teach math. Here is one way to respond to the importance of csc(x):

Cosecant is simply defined as: csc(x) = 1/sin(x)

So, anywhere sin(x) might occur in the “real world”, so does csc(x) since sin(x) = 1/csc(x). You could always rewrite sin(x) in terms of csc(x).

One great importance of csc(x) is that it can abbreviate expressions involving sin(x).

For example, (1/sin(x))^2 = (cos(x)/sin(x))^2 + 1 is more clearly written as

(csc(x))^2 = (cot(x))^2 + 1.

Abbreviations are very useful, they are everywhere in math. A basic example would be the number 8.

It is more convenient to write 8 instead of 1+1+1+1+1+1+1+1. But there is a trade off. Now you need to memorize that 8+1=9. That is, you need to learn more rules. This would not be the case if we just wrote it all out:

(1+1+1+1+1+1+1+1)+1=1+1+1+1+1+1+1+1+1.

The abbreviations 8 and 9 are VERY nice, even though one needs to learn additional rules. Likewise, csc(x) is very nice, just take the time to learn the additional rules that accompany the abbreviation.

Cantor
I agree that the math behind the the function is very important. As far as 1/sinx goes, I guess I could set up equation that it would be easier to use the csc, but I was hoping for a real world example that involved graphing, like using the sine or cosine function with sunrises or using the tangent and a rotating light on the wall.

The only example I can find for csc is the type of high gain antennae but thats a little to complicated for high school.

Homework Helper
Gold Member
Examples for use of secant and cosecant: A few exist in Physics, mechanics at least. You might find a formula relating to friction to be more compactly written using one of those functions. How this relates to actual practice in the real world, unclear.

Russell Berty
The light on the wall can be modified.