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

csc (x) = 5

sec^{2} (x) + tan^{2} (x) - 1 = 0

tan^{2} (x) - 3 tan (x) = 0, 0 \leq x < 2 π

tan (θ) = 10

8 sin (θ) - 5 = 3 sin (θ)

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