What is the general solution for sin(2θ)=0.4 ?

The general solution for sin(2θ)=0.4 is θ=(0.41151…)/2+pin,θ= pi/2-(0.41151…)/2+pin

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sin(2θ)=0.4

sin (2 θ) = 0.4

θ = \frac{0.41151 \dots}{2} + πn, θ = \frac{π}{2} - \frac{0.41151 \dots}{2} + πn

Solution steps

sin (2 θ) = 0.4

Apply trig inverse properties

2 θ = arcsin (0.4) + 2 πn, 2 θ = π - arcsin (0.4) + 2 πn

Solve

2 θ = arcsin (0.4) + 2 πn : θ = \frac{arcsin ( 0.4 )}{2} + πn

Solve

2 θ = π - arcsin (0.4) + 2 πn : θ = \frac{π}{2} - \frac{arcsin ( 0.4 )}{2} + πn

θ = \frac{arcsin ( 0.4 )}{2} + πn, θ = \frac{π}{2} - \frac{arcsin ( 0.4 )}{2} + πn

Show solutions in decimal form

θ = \frac{0.41151 \dots}{2} + πn, θ = \frac{π}{2} - \frac{0.41151 \dots}{2} + πn

0.5 = sin (x) cos (x)

sin (4 x) - cos (4 x) = \frac{1}{2}

tan^{2} (θ) + sec (θ) = - 2

9 csc (x) = 63

sin (x) (cos (x) + 1) = 0

What is the general solution for sin(2θ)=0.4 ?
The general solution for sin(2θ)=0.4 is θ=(0.41151…)/2+pin,θ= pi/2-(0.41151…)/2+pin