What is the general solution for sin(2x)= 1/3 ?

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

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sin(2x)= 1/3

sin (2 x) = \frac{1}{3}

x = \frac{0.33983 \dots}{2} + πn, x = \frac{π}{2} - \frac{0.33983 \dots}{2} + πn

Solution steps

sin (2 x) = \frac{1}{3}

Apply trig inverse properties

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

Solve

2 x = arcsin (\frac{1}{3}) + 2 πn : x = \frac{arcsin ( \frac{1}{3} )}{2} + πn

Solve

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

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

Show solutions in decimal form

x = \frac{0.33983 \dots}{2} + πn, x = \frac{π}{2} - \frac{0.33983 \dots}{2} + πn

4 sin (θ) - 3 = 2 sin (θ)

cos (2 x) = - 0.5

5 cos (x) - 5 sin (x) = 0

32 + 6 sin (x) = 0

5 tan (θ) = 4

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