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受欢迎的三角函数 >

sin(4θ)=0.345

解答

sin (4 θ) = 0.345

解答

θ = \frac{0.35223 \dots}{4} + \frac{πn}{2}, θ = \frac{π}{4} - \frac{0.35223 \dots}{4} + \frac{πn}{2}

+1

度数

θ = 5.04544 \dots^{\circ} + 9 0^{\circ} n, θ = 39.95455 \dots^{\circ} + 9 0^{\circ} n

求解步骤

sin (4 θ) = 0.345

使用反三角函数性质

sin (4 θ) = 0.345

sin (4 θ) = 0.345

的通解

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

4 θ = arcsin (0.345) + 2 πn, 4 θ = π - arcsin (0.345) + 2 πn

4 θ = arcsin (0.345) + 2 πn, 4 θ = π - arcsin (0.345) + 2 πn

解

4 θ = arcsin (0.345) + 2 πn : θ = \frac{arcsin ( 0.345 )}{4} + \frac{πn}{2}

4 θ = arcsin (0.345) + 2 πn

两边除以

4

4 θ = arcsin (0.345) + 2 πn

两边除以

4

\frac{4 θ}{4} = \frac{arcsin ( 0.345 )}{4} + \frac{2 πn}{4}

化简

θ = \frac{arcsin ( 0.345 )}{4} + \frac{πn}{2}

θ = \frac{arcsin ( 0.345 )}{4} + \frac{πn}{2}

解

4 θ = π - arcsin (0.345) + 2 πn : θ = \frac{π}{4} - \frac{arcsin ( 0.345 )}{4} + \frac{πn}{2}

4 θ = π - arcsin (0.345) + 2 πn

两边除以

4

4 θ = π - arcsin (0.345) + 2 πn

两边除以

4

\frac{4 θ}{4} = \frac{π}{4} - \frac{arcsin ( 0.345 )}{4} + \frac{2 πn}{4}

化简

θ = \frac{π}{4} - \frac{arcsin ( 0.345 )}{4} + \frac{πn}{2}

θ = \frac{π}{4} - \frac{arcsin ( 0.345 )}{4} + \frac{πn}{2}

θ = \frac{arcsin ( 0.345 )}{4} + \frac{πn}{2}, θ = \frac{π}{4} - \frac{arcsin ( 0.345 )}{4} + \frac{πn}{2}

以小数形式表示解

θ = \frac{0.35223 \dots}{4} + \frac{πn}{2}, θ = \frac{π}{4} - \frac{0.35223 \dots}{4} + \frac{πn}{2}

作图

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