What is the general solution for sin(x)=(sqrt(5))/3 ?

The general solution for sin(x)=(sqrt(5))/3 is x=0.84106…+2pin,x=pi-0.84106…+2pin

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sin(x)=(sqrt(5))/3

sin (x) = \frac{5}{3}

x = 0.84106 \dots + 2 πn, x = π - 0.84106 \dots + 2 πn

Solution steps

sin (x) = \frac{5}{3}

Apply trig inverse properties

x = arcsin (\frac{5}{3}) + 2 πn, x = π - arcsin (\frac{5}{3}) + 2 πn

Show solutions in decimal form

x = 0.84106 \dots + 2 πn, x = π - 0.84106 \dots + 2 πn

sin (θ) = \frac{3}{4}

2 cos (2 θ) - 1 = 0, 0 \leq θ \leq 2 π

6 cos (x) + 6 sin (x) tan (x) = 12, 0 \leq x \leq 2 π

6 ∣ tan (x) ∣ = 6

cos^{2} (x) + 3 sin^{2} (x) = 1

What is the general solution for sin(x)=(sqrt(5))/3 ?
The general solution for sin(x)=(sqrt(5))/3 is x=0.84106…+2pin,x=pi-0.84106…+2pin