perplexus.info :: Just Math : Sine in Exponent

Sine in Exponent (Posted on 2019-04-03)

Find the smallest positive integer x satisfying the equation below.

2^{sin x} + 3^{sin x} + 6^{sin x} = 1

No Solution Yet Submitted by Danish Ahmed Khan

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2 possible solutions

| Comment 1 of 17

Since 1/2+1/3+1/6=1, sin(x)=-1

In radians x=pi (or 3pi/2 + n*2pi for integer n) but this is never an integer.

In degrees x=270 (or 270 + 360n) and the smallest positive integer is 270.

Edited on April 3, 2019, 2:35 pm

Posted by Jer on 2019-04-03 11:50:26

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