What is the general solution for sin(x)= 5/19 ?

The general solution for sin(x)= 5/19 is x=0.26629…+2pin,x=pi-0.26629…+2pin

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sin(x)= 5/19

sin (x) = \frac{5}{19}

x = 0.26629 \dots + 2 πn, x = π - 0.26629 \dots + 2 πn

Degrees

x = 15.25752 \dots^{\circ} + 36 0^{\circ} n, x = 164.74247 \dots^{\circ} + 36 0^{\circ} n

Solution steps

sin (x) = \frac{5}{19}

Apply trig inverse properties

sin (x) = \frac{5}{19}

General solutions for

sin (x) = \frac{5}{19}

sin (x) = a \Rightarrow x = arcsin (a) + 2 πn, x = π - arcsin (a) + 2 πn

x = arcsin (\frac{5}{19}) + 2 πn, x = π - arcsin (\frac{5}{19}) + 2 πn

x = arcsin (\frac{5}{19}) + 2 πn, x = π - arcsin (\frac{5}{19}) + 2 πn

Show solutions in decimal form

x = 0.26629 \dots + 2 πn, x = π - 0.26629 \dots + 2 πn

1 = 3 sin (\frac{π}{4} (x - 5)) + 5

sin (x + π) - sin (x) - 1 = 0

4 sin^{2} (x) + 2 sin (x) = 0

tan (x) = 3, - \frac{π}{3} \leq x \leq \frac{3 π}{2}

sin (x) = \frac{5}{16}

What is the general solution for sin(x)= 5/19 ?
The general solution for sin(x)= 5/19 is x=0.26629…+2pin,x=pi-0.26629…+2pin