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受欢迎的三角函数 >

sin(θ/2)=0.4

解答

sin (\frac{θ}{2}) = 0.4

解答

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

+1

度数

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

求解步骤

sin (\frac{θ}{2}) = 0.4

使用反三角函数性质

sin (\frac{θ}{2}) = 0.4

sin (\frac{θ}{2}) = 0.4

的通解

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

解

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

\frac{θ}{2} = arcsin (0.4) + 2 πn

在两边乘以

2

\frac{θ}{2} = arcsin (0.4) + 2 πn

在两边乘以

2

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

化简

θ = 2 arcsin (0.4) + 4 πn

θ = 2 arcsin (0.4) + 4 πn

解

\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

在两边乘以

2

\frac{θ}{2} = π - arcsin (0.4) + 2 πn

在两边乘以

2

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

化简

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

以小数形式表示解

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

作图

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