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受欢迎的三角函数 >

sin(2x+30)=0.8

解答

sin (2 x + 30) = 0.8

解答

x = - 15 + πn + \frac{0.92729 \dots}{2}, x = πn + \frac{π}{2} - \frac{0.92729 \dots}{2} - 15

+1

度数

x = - 832.87164 \dots^{\circ} + 18 0^{\circ} n, x = - 796.00174 \dots^{\circ} + 18 0^{\circ} n

求解步骤

sin (2 x + 30) = 0.8

使用反三角函数性质

sin (2 x + 30) = 0.8

sin (2 x + 30) = 0.8

的通解

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

2 x + 30 = arcsin (0.8) + 2 πn, 2 x + 30 = π - arcsin (0.8) + 2 πn

2 x + 30 = arcsin (0.8) + 2 πn, 2 x + 30 = π - arcsin (0.8) + 2 πn

解

2 x + 30 = arcsin (0.8) + 2 πn : x = - 15 + πn + \frac{arcsin ( 0.8 )}{2}

2 x + 30 = arcsin (0.8) + 2 πn

将

30

到右边

2 x + 30 = arcsin (0.8) + 2 πn

两边减去

30

2 x + 30 - 30 = arcsin (0.8) + 2 πn - 30

化简

2 x = arcsin (0.8) + 2 πn - 30

2 x = arcsin (0.8) + 2 πn - 30

两边除以

2

2 x = arcsin (0.8) + 2 πn - 30

两边除以

2

\frac{2 x}{2} = \frac{arcsin ( 0.8 )}{2} + \frac{2 πn}{2} - \frac{30}{2}

化简

\frac{2 x}{2} = \frac{arcsin ( 0.8 )}{2} + \frac{2 πn}{2} - \frac{30}{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 ( 0.8 )}{2} + \frac{2 πn}{2} - \frac{30}{2} : - 15 + πn + \frac{arcsin ( 0.8 )}{2}

\frac{arcsin ( 0.8 )}{2} + \frac{2 πn}{2} - \frac{30}{2}

对同类项分组

= - \frac{30}{2} + \frac{2 πn}{2} + \frac{arcsin ( 0.8 )}{2}

数字相除:

\frac{30}{2} = 15

= - 15 + \frac{2 πn}{2} + \frac{arcsin ( 0.8 )}{2}

数字相除:

\frac{2}{2} = 1

= - 15 + πn + \frac{arcsin ( 0.8 )}{2}

x = - 15 + πn + \frac{arcsin ( 0.8 )}{2}

x = - 15 + πn + \frac{arcsin ( 0.8 )}{2}

x = - 15 + πn + \frac{arcsin ( 0.8 )}{2}

解

2 x + 30 = π - arcsin (0.8) + 2 πn : x = πn + \frac{π}{2} - \frac{arcsin ( 0.8 )}{2} - 15

2 x + 30 = π - arcsin (0.8) + 2 πn

将

30

到右边

2 x + 30 = π - arcsin (0.8) + 2 πn

两边减去

30

2 x + 30 - 30 = π - arcsin (0.8) + 2 πn - 30

化简

2 x = π - arcsin (0.8) + 2 πn - 30

2 x = π - arcsin (0.8) + 2 πn - 30

两边除以

2

2 x = π - arcsin (0.8) + 2 πn - 30

两边除以

2

\frac{2 x}{2} = \frac{π}{2} - \frac{arcsin ( 0.8 )}{2} + \frac{2 πn}{2} - \frac{30}{2}

化简

\frac{2 x}{2} = \frac{π}{2} - \frac{arcsin ( 0.8 )}{2} + \frac{2 πn}{2} - \frac{30}{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 ( 0.8 )}{2} + \frac{2 πn}{2} - \frac{30}{2} : πn + \frac{π}{2} - \frac{arcsin ( 0.8 )}{2} - 15

\frac{π}{2} - \frac{arcsin ( 0.8 )}{2} + \frac{2 πn}{2} - \frac{30}{2}

对同类项分组

= \frac{π}{2} - \frac{30}{2} + \frac{2 πn}{2} - \frac{arcsin ( 0.8 )}{2}

数字相除:

\frac{30}{2} = 15

= \frac{π}{2} - 15 + \frac{2 πn}{2} - \frac{arcsin ( 0.8 )}{2}

数字相除:

\frac{2}{2} = 1

= \frac{π}{2} - 15 + πn - \frac{arcsin ( 0.8 )}{2}

对同类项分组

= πn + \frac{π}{2} - \frac{arcsin ( 0.8 )}{2} - 15

x = πn + \frac{π}{2} - \frac{arcsin ( 0.8 )}{2} - 15

x = πn + \frac{π}{2} - \frac{arcsin ( 0.8 )}{2} - 15

x = πn + \frac{π}{2} - \frac{arcsin ( 0.8 )}{2} - 15

x = - 15 + πn + \frac{arcsin ( 0.8 )}{2}, x = πn + \frac{π}{2} - \frac{arcsin ( 0.8 )}{2} - 15

以小数形式表示解

x = - 15 + πn + \frac{0.92729 \dots}{2}, x = πn + \frac{π}{2} - \frac{0.92729 \dots}{2} - 15

作图

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