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Minimizing Trigo value (Posted on 2014-03-02) Difficulty: 3 of 5
Find the minimum value of | sin x + cos x + tan x + cot x + sec x + csc x | for any real number x.

No Solution Yet Submitted by Danish Ahmed Khan    
Rating: 4.0000 (2 votes)

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re(3): answer | Comment 5 of 7 |
(In reply to re(2): answer by Ady TZIDON)

Interesting question.

 I could see from plotting the given expression that the |sum| was tantalisingly close to 2*2^(1/2)-1. But as you note, the value of x, near 2.65345, looks esoteric, until one realises, with effort, that x = pi-arcsin((sin(x)), plugging in the value of sin(x) given above; from which x can be determined with any desired degree of accuracy.

Edited on March 3, 2014, 12:48 am
  Posted by broll on 2014-03-03 00:37:24

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