What is the purpose of the cotangent, secant, and cosecant?

1 Answer
Jim H
Aug 24, 2015

I can think right now, of two purposes.

Explanation:

Naming Ratios
For 3 numbers there are 6 ratios that can be made. Sine, Cosine and Tangent name 3 of the ratios, and the three you mentioned allow us to name all 6 ratios.

Avoiding division.

Example:
If we know that the angle of elevation to the top of a 12 meter tall building is 40^@ and we want to find the distance to the building, call it x we could use 12/x = tan40^@ so x = 12/tan40^@ Now we get a decimal approximation for tan40^@ ~~ 0.8391 and do the division.

OR use x/12 = cot40^@ so x = 12cot40^@ =

We get cot40^@ ~~ 1.1918 and multiply.

Also, in calculus many of us prefer to work with multiplication of functions rather than division and prefer, for example,

y = x^3cotx rather than y = x^3/tanx

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