What is the general solution for sin(x)=(-4)/7 ?

The general solution for sin(x)=(-4)/7 is x=-0.60824…+2pin,x=pi+0.60824…+2pin

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sin(x)=(-4)/7

sin (x) = \frac{- 4}{7}

x = - 0.60824 \dots + 2 πn, x = π + 0.60824 \dots + 2 πn

Solution steps

sin (x) = \frac{- 4}{7}

Apply the fraction rule:

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

sin (x) = - \frac{4}{7}

Apply trig inverse properties

x = arcsin (- \frac{4}{7}) + 2 πn, x = π + arcsin (\frac{4}{7}) + 2 πn

Show solutions in decimal form

x = - 0.60824 \dots + 2 πn, x = π + 0.60824 \dots + 2 πn

1 - cos (θ) = \frac{2 π}{3}

0.2727 = sec (2.746 x) - 1

23 sin (2 θ) = 3, 0 \leq θ < 2 π

cos (x) - 3 = 3 cos (x)

2 (1 - cos^{2} (x)) = 1 + cos (x)

What is the general solution for sin(x)=(-4)/7 ?
The general solution for sin(x)=(-4)/7 is x=-0.60824…+2pin,x=pi+0.60824…+2pin