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

The general solution for sin(x)=(sqrt(5))/5 is x=0.46364…+2pin,x=pi-0.46364…+2pin

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

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

x = 0.46364 \dots + 2 πn, x = π - 0.46364 \dots + 2 πn

Solution steps

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

Apply trig inverse properties

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

Show solutions in decimal form

x = 0.46364 \dots + 2 πn, x = π - 0.46364 \dots + 2 πn

tan (θ) = 0.11246

cos (2 θ) - sin^{2} (θ) = 1

sin (x) = \frac{3}{4}

2 sin (2 x) = 3 sin (x)

4 sin (\frac{t}{2}) - 1 = 1, - \frac{π}{2} \leq t \leq \frac{π}{2}

What is the general solution for sin(x)=(sqrt(5))/5 ?
The general solution for sin(x)=(sqrt(5))/5 is x=0.46364…+2pin,x=pi-0.46364…+2pin