How do you solve $2sin (3theta) +1=0$ ?

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Answer 1 · 2015-07-01T00:52:29

Solve f(x) = 2sin 3x + 1 = 0

On the trig unit circle,

sin 3x = - 1/2 -> 3x = 210 deg and 3x = 330 deg

a. 3x = 210 -> $x = 70$ deg
b. 3x = 330 -> $x = 110$ deg

Check:
a. x = 70 deg -> 3x = 210 --> sin 210 = - 1/2 --> 2(-1/2) + 1 = 0. OK
b. x = 110 deg -> 3x = 330--> sin 330 = - 1/2 -> 2(-1/2) + 1 = 0. OK

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