What is the general solution for sin(x)=-1/4 ?

The general solution for sin(x)=-1/4 is x=-0.25268…+2pin,x=pi+0.25268…+2pin

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sin(x)=-1/4

sin (x) = - \frac{1}{4}

x = - 0.25268 \dots + 2 πn, x = π + 0.25268 \dots + 2 πn

Solution steps

sin (x) = - \frac{1}{4}

Apply trig inverse properties

x = arcsin (- \frac{1}{4}) + 2 πn, x = π + arcsin (\frac{1}{4}) + 2 πn

Show solutions in decimal form

x = - 0.25268 \dots + 2 πn, x = π + 0.25268 \dots + 2 πn

sin (x) + cos (2 x) = 0

sin (x) - cos (x) = 2

sin (x) = \frac{3}{2}, 0 \leq x \leq 2 π

2 sin (θ) = 0

- 2 cos (x) = 0

What is the general solution for sin(x)=-1/4 ?
The general solution for sin(x)=-1/4 is x=-0.25268…+2pin,x=pi+0.25268…+2pin