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

The general solution for sin(x)=-2/(sqrt(5)) is x=-1.10714…+2pin,x=pi+1.10714…+2pin

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sin(x)=-2/(sqrt(5))

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

x = - 1.10714 \dots + 2 πn, x = π + 1.10714 \dots + 2 πn

Solution steps

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

Simplify

- \frac{2}{5} : - \frac{2 5}{5}

Apply trig inverse properties

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

Show solutions in decimal form

x = - 1.10714 \dots + 2 πn, x = π + 1.10714 \dots + 2 πn

tan (2 x) = - 1.8

cos (2 x) + sin (2 x) = - 1

5 cot (x) + 3 = - 2

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

3 cos (x) (sin (x) + tan (x)) = 2 (1 + cos (x))

What is the general solution for sin(x)=-2/(sqrt(5)) ?
The general solution for sin(x)=-2/(sqrt(5)) is x=-1.10714…+2pin,x=pi+1.10714…+2pin