What is the general solution for sin(2x)=-(2sqrt(6))/7 ?

The general solution for sin(2x)=-(2sqrt(6))/7 is x=-(0.77519…)/2+pin,x= pi/2+(0.77519…)/2+pin

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sin(2x)=-(2sqrt(6))/7

sin (2 x) = - \frac{2 6}{7}

x = - \frac{0.77519 \dots}{2} + πn, x = \frac{π}{2} + \frac{0.77519 \dots}{2} + πn

Solution steps

sin (2 x) = - \frac{2 6}{7}

Apply trig inverse properties

2 x = arcsin (- \frac{2 6}{7}) + 2 πn, 2 x = π + arcsin (\frac{2 6}{7}) + 2 πn

Solve

2 x = arcsin (- \frac{2 6}{7}) + 2 πn : x = - \frac{arcsin ( \frac{2 6}{7} )}{2} + πn

Solve

2 x = π + arcsin (\frac{2 6}{7}) + 2 πn : x = \frac{π}{2} + \frac{arcsin ( \frac{2 6}{7} )}{2} + πn

x = - \frac{arcsin ( \frac{2 6}{7} )}{2} + πn, x = \frac{π}{2} + \frac{arcsin ( \frac{2 6}{7} )}{2} + πn

Show solutions in decimal form

x = - \frac{0.77519 \dots}{2} + πn, x = \frac{π}{2} + \frac{0.77519 \dots}{2} + πn

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\frac{18 cos ( 2 θ ) + 27 cos ( θ )}{2} = 0

What is the general solution for sin(2x)=-(2sqrt(6))/7 ?
The general solution for sin(2x)=-(2sqrt(6))/7 is x=-(0.77519…)/2+pin,x= pi/2+(0.77519…)/2+pin