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受欢迎的三角函数 >

2sin^3(x)=sin^3(x)

解答

2 sin^{3} (x) = sin^{3} (x)

解答

x = 2 πn, x = π + 2 πn

+1

度数

x = 0^{\circ} + 36 0^{\circ} n, x = 18 0^{\circ} + 36 0^{\circ} n

求解步骤

2 sin^{3} (x) = sin^{3} (x)

用替代法求解

2 sin^{3} (x) = sin^{3} (x)

令

: sin (x) = u

2 u^{3} = u^{3}

2 u^{3} = u^{3} : u = 0

2 u^{3} = u^{3}

将

u^{3}

para o lado esquerdo

2 u^{3} = u^{3}

两边减去

u^{3}

2 u^{3} - u^{3} = u^{3} - u^{3}

化简

u^{3} = 0

u^{3} = 0

使用法则

x^{n} = 0 \Rightarrow x = 0

u = 0

u = sin (x)

代回

sin (x) = 0

sin (x) = 0

sin (x) = 0 : x = 2 πn, x = π + 2 πn

sin (x) = 0

sin (x) = 0

的通解

sin (x)

周期表（周期为

2 πn

"）：

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

x = 0 + 2 πn, x = π + 2 πn

x = 0 + 2 πn, x = π + 2 πn

解

x = 0 + 2 πn : x = 2 πn

x = 0 + 2 πn

0 + 2 πn = 2 πn

x = 2 πn

x = 2 πn, x = π + 2 πn

合并所有解

x = 2 πn, x = π + 2 πn

作图

流行的例子

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-a^2c_{1}cos(ax)-a^2c_{2}sin(ax)=0

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