What is the general solution for 6sin(2x)=4 ?

The general solution for 6sin(2x)=4 is x=(0.72972…)/2+pin,x= pi/2-(0.72972…)/2+pin

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6sin(2x)=4

6 sin (2 x) = 4

x = \frac{0.72972 \dots}{2} + πn, x = \frac{π}{2} - \frac{0.72972 \dots}{2} + πn

Solution steps

6 sin (2 x) = 4

Divide both sides by

6

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

Apply trig inverse properties

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

Solve

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

Solve

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

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

Show solutions in decimal form

x = \frac{0.72972 \dots}{2} + πn, x = \frac{π}{2} - \frac{0.72972 \dots}{2} + πn

cos^{2} (x) + sin (x) = - 1

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

2 sin (2 x) + 3 sin (x) = 0

sin (x) = - \frac{2}{5}

tan (2 x) = - 1.8

What is the general solution for 6sin(2x)=4 ?
The general solution for 6sin(2x)=4 is x=(0.72972…)/2+pin,x= pi/2-(0.72972…)/2+pin