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 >

sin(2x)= pi/6

解答

sin (2 x) = \frac{π}{6}

解答

x = \frac{0.55106 \dots}{2} + πn, x = \frac{π}{2} - \frac{0.55106 \dots}{2} + πn

+1

度数

x = 15.78698 \dots^{\circ} + 18 0^{\circ} n, x = 74.21301 \dots^{\circ} + 18 0^{\circ} n

求解步骤

sin (2 x) = \frac{π}{6}

使用反三角函数性质

sin (2 x) = \frac{π}{6}

sin (2 x) = \frac{π}{6}

的通解

sin (x) = a \Rightarrow x = arcsin (a) + 2 πn, x = π - arcsin (a) + 2 πn

2 x = arcsin (\frac{π}{6}) + 2 πn, 2 x = π - arcsin (\frac{π}{6}) + 2 πn

2 x = arcsin (\frac{π}{6}) + 2 πn, 2 x = π - arcsin (\frac{π}{6}) + 2 πn

解

2 x = arcsin (\frac{π}{6}) + 2 πn : x = \frac{arcsin ( \frac{π}{6} )}{2} + πn

2 x = arcsin (\frac{π}{6}) + 2 πn

两边除以

2

2 x = arcsin (\frac{π}{6}) + 2 πn

两边除以

2

\frac{2 x}{2} = \frac{arcsin ( \frac{π}{6} )}{2} + \frac{2 πn}{2}

化简

x = \frac{arcsin ( \frac{π}{6} )}{2} + πn

x = \frac{arcsin ( \frac{π}{6} )}{2} + πn

解

2 x = π - arcsin (\frac{π}{6}) + 2 πn : x = \frac{π}{2} - \frac{arcsin ( \frac{π}{6} )}{2} + πn

2 x = π - arcsin (\frac{π}{6}) + 2 πn

两边除以

2

2 x = π - arcsin (\frac{π}{6}) + 2 πn

两边除以

2

\frac{2 x}{2} = \frac{π}{2} - \frac{arcsin ( \frac{π}{6} )}{2} + \frac{2 πn}{2}

化简

x = \frac{π}{2} - \frac{arcsin ( \frac{π}{6} )}{2} + πn

x = \frac{π}{2} - \frac{arcsin ( \frac{π}{6} )}{2} + πn

x = \frac{arcsin ( \frac{π}{6} )}{2} + πn, x = \frac{π}{2} - \frac{arcsin ( \frac{π}{6} )}{2} + πn

以小数形式表示解

x = \frac{0.55106 \dots}{2} + πn, x = \frac{π}{2} - \frac{0.55106 \dots}{2} + πn

作图

流行的例子

sin(x)= 8/17 sin(2x)

sin (x) = \frac{8}{17} sin (2 x)

2 = 1 + sin (2 x)

cosh (x - 1) = 2

tan (x) = \frac{7}{25}

tan(x)=-1,0<x<2pi

tan (x) = - 1, 0 < x < 2 π