How do you solve $Sin(x) = -(1/2)$ ?

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Answer 1 · 2018-04-08T23:05:30

$x=(7pi)/6+2pin, x=(11pi)/6+2pin$

Examine the unit circle to see where the sine is $-1/2.$

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$x=(7pi)/6, x=(11pi)/6$ give the desired value. But sine is periodic, all values of sine repeat every $2pi$ units.

To account for that we'll add $2pin$ to each answer where $n$ is any integer.

$x=(7pi)/6+2pin, x=(11pi)/6+2pin$

How do you solve Sin(x) = -(1/2)Sin(x) = -(1/2)?