What is the general solution for sin(2x)=0.8 ?

The general solution for sin(2x)=0.8 is x=(0.92729…)/2+pin,x= pi/2-(0.92729…)/2+pin

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sin(2x)=0.8

sin (2 x) = 0.8

x = \frac{0.92729 \dots}{2} + πn, x = \frac{π}{2} - \frac{0.92729 \dots}{2} + πn

Solution steps

sin (2 x) = 0.8

Apply trig inverse properties

2 x = arcsin (0.8) + 2 πn, 2 x = π - arcsin (0.8) + 2 πn

Solve

2 x = arcsin (0.8) + 2 πn : x = \frac{arcsin ( 0.8 )}{2} + πn

Solve

2 x = π - arcsin (0.8) + 2 πn : x = \frac{π}{2} - \frac{arcsin ( 0.8 )}{2} + πn

x = \frac{arcsin ( 0.8 )}{2} + πn, x = \frac{π}{2} - \frac{arcsin ( 0.8 )}{2} + πn

Show solutions in decimal form

x = \frac{0.92729 \dots}{2} + πn, x = \frac{π}{2} - \frac{0.92729 \dots}{2} + πn

cot (x) = tan (x)

2 sin^{2} (x) + 3 = 0

3 tan (\frac{x}{2}) - 3 = 0

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

8 cos^{2} (x) + 10 cos (x) + 3 = 0

What is the general solution for sin(2x)=0.8 ?
The general solution for sin(2x)=0.8 is x=(0.92729…)/2+pin,x= pi/2-(0.92729…)/2+pin