Interview Question: Trigonometric Basics

Sample Question #137 (mathematics – geometry)

Find the integral of the following trigonometric functions:

  1. sin x
  2. cos x
  3. tan x
  4. 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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One Response to Interview Question: Trigonometric Basics

  1. Brett says:

    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.
     

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