The following equation sin &#x2061;<!-- ⁡ --> ( x + &#x03C0;<!-- π --> 4 </

Wade Bullock

Wade Bullock

Answered question

2022-07-01

The following equation
sin ( x + π 4 ) = sin ( 3 8 π 3 x )

Answer & Explanation

Gustavo Brady

Gustavo Brady

Beginner2022-07-02Added 9 answers

The equality sin α = sin β is equivalent to the condition
α = β + 2 k π or α = π β + 2 k π
(where k is an integer). So in your case you have
x + π 4 = 3 π 8 3 x + 2 k π
which gives
x = π 32 + k π 2
or the other branch
x + π 4 = π 3 π 8 + 3 x + 2 k π
that yields
x = 3 π 16 k π
that you can also write as
x = 3 π 16 + k π
since k can be an arbitrary integer.
Can you group into just the first solution set? You'd need to write
3 π 16 = π 32 + k π 2
for some integer k, but the equation gives
6 = 1 + 16 k
that has no integer solution.

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