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受欢迎的三角函数 >

0=sin(4x)

解答

0 = sin (4 x)

解答

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

+1

度数

x = 0^{\circ} + 9 0^{\circ} n, x = 4 5^{\circ} + 9 0^{\circ} n

求解步骤

0 = sin (4 x)

交换两边

sin (4 x) = 0

sin (4 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}

4 x = 0 + 2 πn, 4 x = π + 2 πn

4 x = 0 + 2 πn, 4 x = π + 2 πn

解

4 x = 0 + 2 πn : x = \frac{πn}{2}

4 x = 0 + 2 πn

0 + 2 πn = 2 πn

4 x = 2 πn

两边除以

4

4 x = 2 πn

两边除以

4

\frac{4 x}{4} = \frac{2 πn}{4}

化简

x = \frac{πn}{2}

x = \frac{πn}{2}

解

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

4 x = π + 2 πn

两边除以

4

4 x = π + 2 πn

两边除以

4

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

化简

x = \frac{π}{4} + \frac{πn}{2}

x = \frac{π}{4} + \frac{πn}{2}

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

作图

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