What is the general solution for sin(x)= 1/3 ?

The general solution for sin(x)= 1/3 is x=0.33983…+2pin,x=pi-0.33983…+2pin

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sin(x)= 1/3

sin (x) = \frac{1}{3}

x = 0.33983 \dots + 2 πn, x = π - 0.33983 \dots + 2 πn

Solution steps

sin (x) = \frac{1}{3}

Apply trig inverse properties

x = arcsin (\frac{1}{3}) + 2 πn, x = π - arcsin (\frac{1}{3}) + 2 πn

Show solutions in decimal form

x = 0.33983 \dots + 2 πn, x = π - 0.33983 \dots + 2 πn

2 cos^{2} (x) - 3 cos (x) = 0

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

tan (2 x) = 1

sin (4 x) = 0

sec (x) - 2 = 0

What is the general solution for sin(x)= 1/3 ?
The general solution for sin(x)= 1/3 is x=0.33983…+2pin,x=pi-0.33983…+2pin