Many Sine

Algebra Level 2

Find the number of real solutions in the range [ 0 , 100 ] [0,100] of the equation:

sin sin sin sin ⋯ ⋯ ⋯ sin sin sin x = 0 \text{sin sin sin sin }\cdots\cdots\cdots\text{ sin sin sin }x = 0


The answer is 32.

Shikhar Srivastava by Shikhar Srivastava , 22, India

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1 solution

Tom Engelsman
Apr 22, 2020

The solution set is just x = k π , k = 0 , 1 , 2 , . . . , 31 x = k \pi, k = 0, 1, 2, ... , 31 . Hence 32 solutions for the sine composition.

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