What is the general solution for 3+sin(2x)=1-6sin(2x) ?

The general solution for 3+sin(2x)=1-6sin(2x) is x=-(0.28975…)/2+pin,x= pi/2+(0.28975…)/2+pin

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3+sin(2x)=1-6sin(2x)

3 + sin (2 x) = 1 - 6 sin (2 x)

x = - \frac{0.28975 \dots}{2} + πn, x = \frac{π}{2} + \frac{0.28975 \dots}{2} + πn

Solution steps

3 + sin (2 x) = 1 - 6 sin (2 x)

Solve by substitution

sin (2 x) = - \frac{2}{7}

sin (2 x) = - \frac{2}{7} : x = - \frac{arcsin ( \frac{2}{7} )}{2} + πn, x = \frac{π}{2} + \frac{arcsin ( \frac{2}{7} )}{2} + πn

Combine all the solutions

x = - \frac{arcsin ( \frac{2}{7} )}{2} + πn, x = \frac{π}{2} + \frac{arcsin ( \frac{2}{7} )}{2} + πn

Show solutions in decimal form

x = - \frac{0.28975 \dots}{2} + πn, x = \frac{π}{2} + \frac{0.28975 \dots}{2} + πn

cos (x) = 0, sin (x) = cos (x), sin (x) = 0

2 a sin (x) + a = 0

tan (θ) = (\frac{2}{3})

tan (θ) = 8.1443

4 sin (x) = 5 cos (x)

What is the general solution for 3+sin(2x)=1-6sin(2x) ?
The general solution for 3+sin(2x)=1-6sin(2x) is x=-(0.28975…)/2+pin,x= pi/2+(0.28975…)/2+pin