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-10)= 3/7

解答

sin (2 x - 10) = \frac{3}{7}

解答

x = 5 + πn + \frac{0.44291 \dots}{2}, x = πn + \frac{π}{2} - \frac{0.44291 \dots}{2} + 5

+1

度数

x = 299.16736 \dots^{\circ} + 18 0^{\circ} n, x = 363.79043 \dots^{\circ} + 18 0^{\circ} n

求解步骤

sin (2 x - 10) = \frac{3}{7}

使用反三角函数性质

sin (2 x - 10) = \frac{3}{7}

sin (2 x - 10) = \frac{3}{7}

的通解

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

2 x - 10 = arcsin (\frac{3}{7}) + 2 πn, 2 x - 10 = π - arcsin (\frac{3}{7}) + 2 πn

2 x - 10 = arcsin (\frac{3}{7}) + 2 πn, 2 x - 10 = π - arcsin (\frac{3}{7}) + 2 πn

解

2 x - 10 = arcsin (\frac{3}{7}) + 2 πn : x = 5 + πn + \frac{arcsin ( \frac{3}{7} )}{2}

2 x - 10 = arcsin (\frac{3}{7}) + 2 πn

将

10

到右边

2 x - 10 = arcsin (\frac{3}{7}) + 2 πn

两边加上

10

2 x - 10 + 10 = arcsin (\frac{3}{7}) + 2 πn + 10

化简

2 x = arcsin (\frac{3}{7}) + 2 πn + 10

2 x = arcsin (\frac{3}{7}) + 2 πn + 10

两边除以

2

2 x = arcsin (\frac{3}{7}) + 2 πn + 10

两边除以

2

\frac{2 x}{2} = \frac{arcsin ( \frac{3}{7} )}{2} + \frac{2 πn}{2} + \frac{10}{2}

化简

\frac{2 x}{2} = \frac{arcsin ( \frac{3}{7} )}{2} + \frac{2 πn}{2} + \frac{10}{2}

化简

\frac{2 x}{2} : x

\frac{2 x}{2}

数字相除:

\frac{2}{2} = 1

= x

化简

\frac{arcsin ( \frac{3}{7} )}{2} + \frac{2 πn}{2} + \frac{10}{2} : 5 + πn + \frac{arcsin ( \frac{3}{7} )}{2}

\frac{arcsin ( \frac{3}{7} )}{2} + \frac{2 πn}{2} + \frac{10}{2}

对同类项分组

= \frac{10}{2} + \frac{2 πn}{2} + \frac{arcsin ( \frac{3}{7} )}{2}

数字相除:

\frac{10}{2} = 5

= 5 + \frac{2 πn}{2} + \frac{arcsin ( \frac{3}{7} )}{2}

数字相除:

\frac{2}{2} = 1

= 5 + πn + \frac{arcsin ( \frac{3}{7} )}{2}

x = 5 + πn + \frac{arcsin ( \frac{3}{7} )}{2}

x = 5 + πn + \frac{arcsin ( \frac{3}{7} )}{2}

x = 5 + πn + \frac{arcsin ( \frac{3}{7} )}{2}

解

2 x - 10 = π - arcsin (\frac{3}{7}) + 2 πn : x = πn + \frac{π}{2} - \frac{arcsin ( \frac{3}{7} )}{2} + 5

2 x - 10 = π - arcsin (\frac{3}{7}) + 2 πn

将

10

到右边

2 x - 10 = π - arcsin (\frac{3}{7}) + 2 πn

两边加上

10

2 x - 10 + 10 = π - arcsin (\frac{3}{7}) + 2 πn + 10

化简

2 x = π - arcsin (\frac{3}{7}) + 2 πn + 10

2 x = π - arcsin (\frac{3}{7}) + 2 πn + 10

两边除以

2

2 x = π - arcsin (\frac{3}{7}) + 2 πn + 10

两边除以

2

\frac{2 x}{2} = \frac{π}{2} - \frac{arcsin ( \frac{3}{7} )}{2} + \frac{2 πn}{2} + \frac{10}{2}

化简

\frac{2 x}{2} = \frac{π}{2} - \frac{arcsin ( \frac{3}{7} )}{2} + \frac{2 πn}{2} + \frac{10}{2}

化简

\frac{2 x}{2} : x

\frac{2 x}{2}

数字相除:

\frac{2}{2} = 1

= x

化简

\frac{π}{2} - \frac{arcsin ( \frac{3}{7} )}{2} + \frac{2 πn}{2} + \frac{10}{2} : πn + \frac{π}{2} - \frac{arcsin ( \frac{3}{7} )}{2} + 5

\frac{π}{2} - \frac{arcsin ( \frac{3}{7} )}{2} + \frac{2 πn}{2} + \frac{10}{2}

对同类项分组

= \frac{π}{2} + \frac{10}{2} + \frac{2 πn}{2} - \frac{arcsin ( \frac{3}{7} )}{2}

数字相除:

\frac{10}{2} = 5

= \frac{π}{2} + 5 + \frac{2 πn}{2} - \frac{arcsin ( \frac{3}{7} )}{2}

数字相除:

\frac{2}{2} = 1

= \frac{π}{2} + 5 + πn - \frac{arcsin ( \frac{3}{7} )}{2}

对同类项分组

= πn + \frac{π}{2} - \frac{arcsin ( \frac{3}{7} )}{2} + 5

x = πn + \frac{π}{2} - \frac{arcsin ( \frac{3}{7} )}{2} + 5

x = πn + \frac{π}{2} - \frac{arcsin ( \frac{3}{7} )}{2} + 5

x = πn + \frac{π}{2} - \frac{arcsin ( \frac{3}{7} )}{2} + 5

x = 5 + πn + \frac{arcsin ( \frac{3}{7} )}{2}, x = πn + \frac{π}{2} - \frac{arcsin ( \frac{3}{7} )}{2} + 5

以小数形式表示解

x = 5 + πn + \frac{0.44291 \dots}{2}, x = πn + \frac{π}{2} - \frac{0.44291 \dots}{2} + 5

作图

流行的例子

2cos^2(θ)+3sin(θ)=3

2 cos^{2} (θ) + 3 sin (θ) = 3

sin(5x)+sin(3x)=0

sin (5 x) + sin (3 x) = 0

sin (θ) = \frac{1}{7}

2cos^2(x)-5cos(x)=3

2 cos^{2} (x) - 5 cos (x) = 3

4 arctan (x) = π