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

The general solution for sin(θ/2)=0.4 is θ=2*0.41151…+4pin,θ=2pi-2*0.41151…+4pin

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sin(θ/2)=0.4

sin (\frac{θ}{2}) = 0.4

θ = 2 \cdot 0.41151 \dots + 4 πn, θ = 2 π - 2 \cdot 0.41151 \dots + 4 πn

Solution steps

sin (\frac{θ}{2}) = 0.4

Apply trig inverse properties

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

Solve

\frac{θ}{2} = arcsin (0.4) + 2 πn : θ = 2 arcsin (0.4) + 4 πn

Solve

\frac{θ}{2} = π - arcsin (0.4) + 2 πn : θ = 2 π - 2 arcsin (0.4) + 4 πn

θ = 2 arcsin (0.4) + 4 πn, θ = 2 π - 2 arcsin (0.4) + 4 πn

Show solutions in decimal form

θ = 2 \cdot 0.41151 \dots + 4 πn, θ = 2 π - 2 \cdot 0.41151 \dots + 4 πn

arccos (x) = \frac{79}{9 70}

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

50 sec^{2} (5 x) tan (5 x) = 25 + tan^{2} (5 x)

cot (x) = 8

tan (θ) = \frac{- 1}{6}

What is the general solution for sin(θ/2)=0.4 ?
The general solution for sin(θ/2)=0.4 is θ=2*0.41151…+4pin,θ=2pi-2*0.41151…+4pin