zs

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

受欢迎的三角函数 >

cos(pix)=0

解答

cos (π x) = 0

解答

x = \frac{1}{2} + 2 n, x = \frac{3}{2} + 2 n

+1

度数

x = 28.64788 \dots^{\circ} + 114.59155 \dots^{\circ} n, x = 85.94366 \dots^{\circ} + 114.59155 \dots^{\circ} n

求解步骤

cos (π x) = 0

cos (π x) = 0

的通解

cos (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} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{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} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

π x = \frac{π}{2} + 2 πn, π x = \frac{3 π}{2} + 2 πn

π x = \frac{π}{2} + 2 πn, π x = \frac{3 π}{2} + 2 πn

解

π x = \frac{π}{2} + 2 πn : x = \frac{1}{2} + 2 n

π x = \frac{π}{2} + 2 πn

两边除以

π

π x = \frac{π}{2} + 2 πn

两边除以

π

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

化简

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

化简

\frac{π x}{π} : x

\frac{π x}{π}

约分:

π

= x

化简

\frac{\frac{π}{2}}{π} + \frac{2 πn}{π} : \frac{1}{2} + 2 n

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

\frac{\frac{π}{2}}{π} = \frac{1}{2}

\frac{\frac{π}{2}}{π}

使用分式法则:

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

= \frac{π}{2 π}

约分:

π

= \frac{1}{2}

\frac{2 πn}{π} = 2 n

\frac{2 πn}{π}

约分:

π

= 2 n

= \frac{1}{2} + 2 n

x = \frac{1}{2} + 2 n

x = \frac{1}{2} + 2 n

x = \frac{1}{2} + 2 n

解

π x = \frac{3 π}{2} + 2 πn : x = \frac{3}{2} + 2 n

π x = \frac{3 π}{2} + 2 πn

两边除以

π

π x = \frac{3 π}{2} + 2 πn

两边除以

π

\frac{π x}{π} = \frac{\frac{3 π}{2}}{π} + \frac{2 πn}{π}

化简

\frac{π x}{π} = \frac{\frac{3 π}{2}}{π} + \frac{2 πn}{π}

化简

\frac{π x}{π} : x

\frac{π x}{π}

约分:

π

= x

化简

\frac{\frac{3 π}{2}}{π} + \frac{2 πn}{π} : \frac{3}{2} + 2 n

\frac{\frac{3 π}{2}}{π} + \frac{2 πn}{π}

\frac{\frac{3 π}{2}}{π} = \frac{3}{2}

\frac{\frac{3 π}{2}}{π}

使用分式法则:

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

= \frac{3 π}{2 π}

约分:

π

= \frac{3}{2}

\frac{2 πn}{π} = 2 n

\frac{2 πn}{π}

约分:

π

= 2 n

= \frac{3}{2} + 2 n

x = \frac{3}{2} + 2 n

x = \frac{3}{2} + 2 n

x = \frac{3}{2} + 2 n

x = \frac{1}{2} + 2 n, x = \frac{3}{2} + 2 n

作图

流行的例子

cos^{3} (0)

cos^2(x)-sin^2(x)=sin(x)

cos^{2} (x) - sin^{2} (x) = sin (x)

cos (24 0^{\circ})

arcsin(sin((7pi)/6))

arcsin (sin (\frac{7 π}{6}))

cos(arcsin(4/5))

cos (arcsin (\frac{4}{5}))