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受欢迎的三角函数 >

sin(pix)=-1/2

解答

sin (π x) = - \frac{1}{2}

解答

x = \frac{7}{6} + 2 n, x = \frac{11}{6} + 2 n

+1

度数

x = 66.84507 \dots^{\circ} + 114.59155 \dots^{\circ} n, x = 105.04226 \dots^{\circ} + 114.59155 \dots^{\circ} n

求解步骤

sin (π x) = - \frac{1}{2}

sin (π x) = - \frac{1}{2}

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}

π x = \frac{7 π}{6} + 2 πn, π x = \frac{11 π}{6} + 2 πn

π x = \frac{7 π}{6} + 2 πn, π x = \frac{11 π}{6} + 2 πn

解

π x = \frac{7 π}{6} + 2 πn : x = \frac{7}{6} + 2 n

π x = \frac{7 π}{6} + 2 πn

两边除以

π

π x = \frac{7 π}{6} + 2 πn

两边除以

π

\frac{π x}{π} = \frac{\frac{7 π}{6}}{π} + \frac{2 πn}{π}

化简

\frac{π x}{π} = \frac{\frac{7 π}{6}}{π} + \frac{2 πn}{π}

化简

\frac{π x}{π} : x

\frac{π x}{π}

约分:

π

= x

化简

\frac{\frac{7 π}{6}}{π} + \frac{2 πn}{π} : \frac{7}{6} + 2 n

\frac{\frac{7 π}{6}}{π} + \frac{2 πn}{π}

\frac{\frac{7 π}{6}}{π} = \frac{7}{6}

\frac{\frac{7 π}{6}}{π}

使用分式法则:

\frac{\frac{b}{c}}{a} = \frac{b}{c \cdot a}

= \frac{7 π}{6 π}

约分:

π

= \frac{7}{6}

\frac{2 πn}{π} = 2 n

\frac{2 πn}{π}

约分:

π

= 2 n

= \frac{7}{6} + 2 n

x = \frac{7}{6} + 2 n

x = \frac{7}{6} + 2 n

x = \frac{7}{6} + 2 n

解

π x = \frac{11 π}{6} + 2 πn : x = \frac{11}{6} + 2 n

π x = \frac{11 π}{6} + 2 πn

两边除以

π

π x = \frac{11 π}{6} + 2 πn

两边除以

π

\frac{π x}{π} = \frac{\frac{11 π}{6}}{π} + \frac{2 πn}{π}

化简

\frac{π x}{π} = \frac{\frac{11 π}{6}}{π} + \frac{2 πn}{π}

化简

\frac{π x}{π} : x

\frac{π x}{π}

约分:

π

= x

化简

\frac{\frac{11 π}{6}}{π} + \frac{2 πn}{π} : \frac{11}{6} + 2 n

\frac{\frac{11 π}{6}}{π} + \frac{2 πn}{π}

\frac{\frac{11 π}{6}}{π} = \frac{11}{6}

\frac{\frac{11 π}{6}}{π}

使用分式法则:

\frac{\frac{b}{c}}{a} = \frac{b}{c \cdot a}

= \frac{11 π}{6 π}

约分:

π

= \frac{11}{6}

\frac{2 πn}{π} = 2 n

\frac{2 πn}{π}

约分:

π

= 2 n

= \frac{11}{6} + 2 n

x = \frac{11}{6} + 2 n

x = \frac{11}{6} + 2 n

x = \frac{11}{6} + 2 n

x = \frac{7}{6} + 2 n, x = \frac{11}{6} + 2 n

作图

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