How do you solve $sin (3 x) = - 1$ $sin(3x)=-1$ and find all exact general solutions?

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Answer 1 · 2016-10-29T15:12:59

$sin (3 x) = - 1 \to 3 x = {sin}^{- 1} (- 1)$ $sin(3x) = -1 -> 3x = sin^-1(-1)$

$3 x = \frac{3 π}{2} + 2 π n$ $3x = (3pi)/2 + 2pin$

$x = \frac{π}{2} + \frac{2 π n}{3}$ $x = pi/2 + (2pin)/3$

$x = \frac{3 π + 4 π n}{6}$ $x = (3pi + 4pin)/6$

Practice Exercises:

a) $cos (2 x) = - \frac{\sqrt{3}}{2}$ $cos(2x) = -sqrt(3)/2$

b) $tan (4 x) = - 1$ $tan(4x) = -1$

Hopefully this helps!

How do you solve sin(3x)=-1sin(3x)=−1sin(3x)=-1 and find all exact general solutions?