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受欢迎的三角函数 >

sin((5x)/2)=0

解答

sin (\frac{5 x}{2}) = 0

解答

x = \frac{4 πn}{5}, x = \frac{2 π}{5} + \frac{4 πn}{5}

+1

度数

x = 0^{\circ} + 14 4^{\circ} n, x = 7 2^{\circ} + 14 4^{\circ} n

求解步骤

sin (\frac{5 x}{2}) = 0

sin (\frac{5 x}{2}) = 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}

\frac{5 x}{2} = 0 + 2 πn, \frac{5 x}{2} = π + 2 πn

\frac{5 x}{2} = 0 + 2 πn, \frac{5 x}{2} = π + 2 πn

解

\frac{5 x}{2} = 0 + 2 πn : x = \frac{4 πn}{5}

\frac{5 x}{2} = 0 + 2 πn

0 + 2 πn = 2 πn

\frac{5 x}{2} = 2 πn

在两边乘以

2

\frac{5 x}{2} = 2 πn

在两边乘以

2

\frac{2 \cdot 5 x}{2} = 2 \cdot 2 πn

化简

5 x = 4 πn

5 x = 4 πn

两边除以

5

5 x = 4 πn

两边除以

5

\frac{5 x}{5} = \frac{4 πn}{5}

化简

x = \frac{4 πn}{5}

x = \frac{4 πn}{5}

解

\frac{5 x}{2} = π + 2 πn : x = \frac{2 π}{5} + \frac{4 πn}{5}

\frac{5 x}{2} = π + 2 πn

在两边乘以

2

\frac{5 x}{2} = π + 2 πn

在两边乘以

2

\frac{2 \cdot 5 x}{2} = 2 π + 2 \cdot 2 πn

化简

5 x = 2 π + 4 πn

5 x = 2 π + 4 πn

两边除以

5

5 x = 2 π + 4 πn

两边除以

5

\frac{5 x}{5} = \frac{2 π}{5} + \frac{4 πn}{5}

化简

x = \frac{2 π}{5} + \frac{4 πn}{5}

x = \frac{2 π}{5} + \frac{4 πn}{5}

x = \frac{4 πn}{5}, x = \frac{2 π}{5} + \frac{4 πn}{5}

作图

流行的例子

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