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Popular Trigonometria >

sin(θ/2)=0.4

Solução

sin (\frac{θ}{2}) = 0.4

Solução

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

+1

Graus

θ = 47.15635 \dots^{\circ} + 72 0^{\circ} n, θ = 312.84364 \dots^{\circ} + 72 0^{\circ} n

Passos da solução

sin (\frac{θ}{2}) = 0.4

Aplique as propriedades trigonométricas inversas

sin (\frac{θ}{2}) = 0.4

Soluções gerais para

sin (\frac{θ}{2}) = 0.4

sin (x) = a \Rightarrow x = arcsin (a) + 2 πn, x = π - arcsin (a) + 2 πn

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

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

Resolver

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

\frac{θ}{2} = arcsin (0.4) + 2 πn

Multiplicar ambos os lados por

2

\frac{θ}{2} = arcsin (0.4) + 2 πn

Multiplicar ambos os lados por

2

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

Simplificar

θ = 2 arcsin (0.4) + 4 πn

θ = 2 arcsin (0.4) + 4 πn

Resolver

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

\frac{θ}{2} = π - arcsin (0.4) + 2 πn

Multiplicar ambos os lados por

2

\frac{θ}{2} = π - arcsin (0.4) + 2 πn

Multiplicar ambos os lados por

2

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

Simplificar

θ = 2 π - 2 arcsin (0.4) + 4 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

Mostrar soluções na forma decimal

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

Gráfico

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