What is the general solution for sin(x)=-2/5 ?

The general solution for sin(x)=-2/5 is x=-0.41151…+2pin,x=pi+0.41151…+2pin

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sin(x)=-2/5

sin (x) = - \frac{2}{5}

x = - 0.41151 \dots + 2 πn, x = π + 0.41151 \dots + 2 πn

Solution steps

sin (x) = - \frac{2}{5}

Apply trig inverse properties

x = arcsin (- \frac{2}{5}) + 2 πn, x = π + arcsin (\frac{2}{5}) + 2 πn

Show solutions in decimal form

x = - 0.41151 \dots + 2 πn, x = π + 0.41151 \dots + 2 πn

3 sin (x) = 3 sin (x) + 3 cos (x) + 3 sin (x)

2 cos^{2} (x) + 5 sin (x) - 4 = 0

2 cos^{2} (x) - 3 cos (x) = 0

cos^{2} (\frac{x}{2}) - sin^{2} (\frac{x}{2}) = sin (x)

tan (x) + sec (x) = - 1

What is the general solution for sin(x)=-2/5 ?
The general solution for sin(x)=-2/5 is x=-0.41151…+2pin,x=pi+0.41151…+2pin