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

Degrees

x = - 14.47751 \dots^{\circ} + 36 0^{\circ} n, x = 194.47751 \dots^{\circ} + 36 0^{\circ} n

Solution steps

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

Apply the fraction rule:

\frac{- a}{b} = - \frac{a}{b}

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

Apply trig inverse properties

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

General solutions for

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

sin (x) = - a \Rightarrow x = arcsin (- a) + 2 πn, x = π + arcsin (a) + 2 πn

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

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^{4} (x) - sin^{2} (x) = 0

(cos (t) - 4) (2 sin^{2} (t) - 1) = 0

sin (7 5^{\circ}) = \frac{x}{9}

i, 2 cos^{3} (x) + sin (x) + 1 = 2 sin^{2} (x)

t, tan (x) = csc^{2} (x) - 2

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