What is the general solution for sin(2x)=0.3 ?

The general solution for sin(2x)=0.3 is x=(0.30469…)/2+pin,x= pi/2-(0.30469…)/2+pin

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sin(2x)=0.3

sin (2 x) = 0.3

x = \frac{0.30469 \dots}{2} + πn, x = \frac{π}{2} - \frac{0.30469 \dots}{2} + πn

Solution steps

sin (2 x) = 0.3

Apply trig inverse properties

2 x = arcsin (0.3) + 2 πn, 2 x = π - arcsin (0.3) + 2 πn

Solve

2 x = arcsin (0.3) + 2 πn : x = \frac{arcsin ( 0.3 )}{2} + πn

Solve

2 x = π - arcsin (0.3) + 2 πn : x = \frac{π}{2} - \frac{arcsin ( 0.3 )}{2} + πn

x = \frac{arcsin ( 0.3 )}{2} + πn, x = \frac{π}{2} - \frac{arcsin ( 0.3 )}{2} + πn

Show solutions in decimal form

x = \frac{0.30469 \dots}{2} + πn, x = \frac{π}{2} - \frac{0.30469 \dots}{2} + πn

sin (2 x) = 0.6

- 2 cos (t) = 0

4 cos^{2} (θ) - 4 cos (θ) - 3 = 0

4 sin (x) + 3 cos (x) = 2

sec^{2} (x) + 7 tan (x) - 9 = 0

What is the general solution for sin(2x)=0.3 ?
The general solution for sin(2x)=0.3 is x=(0.30469…)/2+pin,x= pi/2-(0.30469…)/2+pin