Sample Question #137 (mathematics – geometry)

Find the integral of the following trigonometric functions:

- sin
*x*
- cos
*x*
- tan
*x*
- sec
*x*

(Comment: I was asked about the integral of cos *x *at a Goldman Sachs interview many years ago and, alas, I had no memory whatsoever of what it should be, and I had no clue how to derive it. As you write out each answer, can you also derive it?)

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ANSWER

Remember, every time you’re asked to do an integral, don’t forget the constant term!

I had to look up the answers on these – and I still don’t remember how to derive them.

1. -cos x + c

2. sin x + c

3. ln |sec x| + c

4. ln |sec x + tan x| + c

Bonus question: what are the 1st derivatives of the trigonometric functions?

BTW, I have never used trigonometry in my work, but I’ve heard some quants do use it in deriving pricing formulas.