What is the general solution for sin(x)= 6/19 ?

The general solution for sin(x)= 6/19 is x=0.32128…+2pin,x=pi-0.32128…+2pin

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sin(x)= 6/19

sin (x) = \frac{6}{19}

x = 0.32128 \dots + 2 πn, x = π - 0.32128 \dots + 2 πn

Solution steps

sin (x) = \frac{6}{19}

Apply trig inverse properties

x = arcsin (\frac{6}{19}) + 2 πn, x = π - arcsin (\frac{6}{19}) + 2 πn

Show solutions in decimal form

x = 0.32128 \dots + 2 πn, x = π - 0.32128 \dots + 2 πn

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

4 sin^{2} (x) - 4 cos^{2} (x) = 23

sec^{2} (θ) = 1

cos (\frac{x + π}{2}) = sin (x)

2 sin (2 x) - 1 = 0, 0 \leq x < 2 π

What is the general solution for sin(x)= 6/19 ?
The general solution for sin(x)= 6/19 is x=0.32128…+2pin,x=pi-0.32128…+2pin