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- Thread starter Cantor
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- #1

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- #2

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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.

- #3

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

- #4

symbolipoint

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How about this: Two people, A and B, standing at a distance of L ft. apart.

Person A stays still. Person B starts running at velocity v in the direction perpendicular to the original line from A to B. Person A measures the angle w from the original line to the line of sight of person B’s position. Then, the distance from A to B at time t is

vtcsc(w) for t,w>0.

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