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 >

20=2.891sin(0.016d-1.183)+18.512

解答

20 = 2.891 sin (0.016 d - 1.183) + 18.512

解答

d = \frac{0.54065 \dots}{0.016} + \frac{2 πn}{0.016} + \frac{1.183}{0.016}, d = \frac{π}{0.016} - \frac{0.54065 \dots}{0.016} + \frac{2 πn}{0.016} + \frac{1.183}{0.016}

+1

度数

d = 6172.39781 \dots^{\circ} + 2250 0^{\circ} n, d = 13550.21558 \dots^{\circ} + 2250 0^{\circ} n

求解步骤

20 = 2.891 sin (0.016 d - 1.183) + 18.512

交换两边

2.891 sin (0.016 d - 1.183) + 18.512 = 20

在两边乘以

1000

2.891 sin (0.016 d - 1.183) + 18.512 = 20

To eliminate decimal points, multiply by 10 for every digit after the decimal pointThere are

3

digits to the right of the decimal point, therefore multiply by

1000

2.891 sin (0.016 d - 1.183) \cdot 1000 + 18.512 \cdot 1000 = 20 \cdot 1000

整理后得

2891 sin (0.016 d - 1.183) + 18512 = 20000

2891 sin (0.016 d - 1.183) + 18512 = 20000

将

18512

到右边

2891 sin (0.016 d - 1.183) + 18512 = 20000

两边减去

18512

2891 sin (0.016 d - 1.183) + 18512 - 18512 = 20000 - 18512

化简

2891 sin (0.016 d - 1.183) = 1488

2891 sin (0.016 d - 1.183) = 1488

两边除以

2891

2891 sin (0.016 d - 1.183) = 1488

两边除以

2891

\frac{2891 sin ( 0.016 d - 1.183 )}{2891} = \frac{1488}{2891}

化简

sin (0.016 d - 1.183) = \frac{1488}{2891}

sin (0.016 d - 1.183) = \frac{1488}{2891}

使用反三角函数性质

sin (0.016 d - 1.183) = \frac{1488}{2891}

sin (0.016 d - 1.183) = \frac{1488}{2891}

的通解

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

0.016 d - 1.183 = arcsin (\frac{1488}{2891}) + 2 πn, 0.016 d - 1.183 = π - arcsin (\frac{1488}{2891}) + 2 πn

0.016 d - 1.183 = arcsin (\frac{1488}{2891}) + 2 πn, 0.016 d - 1.183 = π - arcsin (\frac{1488}{2891}) + 2 πn

解

0.016 d - 1.183 = arcsin (\frac{1488}{2891}) + 2 πn : d = \frac{arcsin ( \frac{1488}{2891} )}{0.016} + \frac{2 πn}{0.016} + \frac{1.183}{0.016}

0.016 d - 1.183 = arcsin (\frac{1488}{2891}) + 2 πn

将

1.183

到右边

0.016 d - 1.183 = arcsin (\frac{1488}{2891}) + 2 πn

两边加上

1.183

0.016 d - 1.183 + 1.183 = arcsin (\frac{1488}{2891}) + 2 πn + 1.183

化简

0.016 d = arcsin (\frac{1488}{2891}) + 2 πn + 1.183

0.016 d = arcsin (\frac{1488}{2891}) + 2 πn + 1.183

两边除以

0.016

0.016 d = arcsin (\frac{1488}{2891}) + 2 πn + 1.183

两边除以

0.016

\frac{0.016 d}{0.016} = \frac{arcsin ( \frac{1488}{2891} )}{0.016} + \frac{2 πn}{0.016} + \frac{1.183}{0.016}

化简

d = \frac{arcsin ( \frac{1488}{2891} )}{0.016} + \frac{2 πn}{0.016} + \frac{1.183}{0.016}

d = \frac{arcsin ( \frac{1488}{2891} )}{0.016} + \frac{2 πn}{0.016} + \frac{1.183}{0.016}

解

0.016 d - 1.183 = π - arcsin (\frac{1488}{2891}) + 2 πn : d = \frac{π}{0.016} - \frac{arcsin ( \frac{1488}{2891} )}{0.016} + \frac{2 πn}{0.016} + \frac{1.183}{0.016}

0.016 d - 1.183 = π - arcsin (\frac{1488}{2891}) + 2 πn

将

1.183

到右边

0.016 d - 1.183 = π - arcsin (\frac{1488}{2891}) + 2 πn

两边加上

1.183

0.016 d - 1.183 + 1.183 = π - arcsin (\frac{1488}{2891}) + 2 πn + 1.183

化简

0.016 d = π - arcsin (\frac{1488}{2891}) + 2 πn + 1.183

0.016 d = π - arcsin (\frac{1488}{2891}) + 2 πn + 1.183

两边除以

0.016

0.016 d = π - arcsin (\frac{1488}{2891}) + 2 πn + 1.183

两边除以

0.016

\frac{0.016 d}{0.016} = \frac{π}{0.016} - \frac{arcsin ( \frac{1488}{2891} )}{0.016} + \frac{2 πn}{0.016} + \frac{1.183}{0.016}

化简

d = \frac{π}{0.016} - \frac{arcsin ( \frac{1488}{2891} )}{0.016} + \frac{2 πn}{0.016} + \frac{1.183}{0.016}

d = \frac{π}{0.016} - \frac{arcsin ( \frac{1488}{2891} )}{0.016} + \frac{2 πn}{0.016} + \frac{1.183}{0.016}

d = \frac{arcsin ( \frac{1488}{2891} )}{0.016} + \frac{2 πn}{0.016} + \frac{1.183}{0.016}, d = \frac{π}{0.016} - \frac{arcsin ( \frac{1488}{2891} )}{0.016} + \frac{2 πn}{0.016} + \frac{1.183}{0.016}

以小数形式表示解

d = \frac{0.54065 \dots}{0.016} + \frac{2 πn}{0.016} + \frac{1.183}{0.016}, d = \frac{π}{0.016} - \frac{0.54065 \dots}{0.016} + \frac{2 πn}{0.016} + \frac{1.183}{0.016}

作图

流行的例子

2sin(θ)=-1,0<= θ<2pi

2 sin (θ) = - 1, 0 \leq θ < 2 π

cos (16 x) = 0

sin(θ)=-(sqrt(35))/6

sin (θ) = - \frac{35}{6}

0.6 = cos (x)

3 tan^{3} (x) - 1 = 0