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

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2 cos^{2} (θ) + 2 sin (θ) - 12 = 9 sin (θ) - 7

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