What is the general solution for solvefor x,sin(x)= 2/3 ?

The general solution for solvefor x,sin(x)= 2/3 is x=0.72972…+2pin,x=pi-0.72972…+2pin

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solvefor x,sin(x)= 2/3

solve for

x, sin (x) = \frac{2}{3}

x = 0.72972 \dots + 2 πn, x = π - 0.72972 \dots + 2 πn

Solution steps

sin (x) = \frac{2}{3}

Apply trig inverse properties

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

Show solutions in decimal form

x = 0.72972 \dots + 2 πn, x = π - 0.72972 \dots + 2 πn

2 sin^{2} (x) = sec (x)

tan (x) = \frac{12}{6}

3 sin (θ) - 2 sin (θ) cos (θ) = 0

\frac{3}{cos ^{2} ( x )} = 3 + 2 tan^{2} (x)

13 \cdot sin (x) = 12

What is the general solution for solvefor x,sin(x)= 2/3 ?
The general solution for solvefor x,sin(x)= 2/3 is x=0.72972…+2pin,x=pi-0.72972…+2pin