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 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

arccos (x) = \frac{8 π}{7}

cos (2 x) = \frac{1}{4}

sin (θ) + 1 = 2 cos^{2} (θ)

sin (x) = \frac{5}{8.8}

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

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