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受欢迎的三角函数 >

2sin(x-10)=-0.4

解答

2 sin (x - 1 0^{\circ}) = - 0.4

解答

x = - 0.20135 \dots + 36 0^{\circ} n + 1 0^{\circ}, x = 18 0^{\circ} + 0.20135 \dots + 36 0^{\circ} n + 1 0^{\circ}

+1

弧度

x = - 0.20135 \dots + \frac{π}{18} + 2 πn, x = π + 0.20135 \dots + \frac{π}{18} + 2 πn

求解步骤

2 sin (x - 1 0^{\circ}) = - 0.4

两边除以

2

2 sin (x - 1 0^{\circ}) = - 0.4

两边除以

2

\frac{2 sin ( x - 1 0 ^{\circ} )}{2} = \frac{- 0.4}{2}

化简

\frac{2 sin ( x - 1 0 ^{\circ} )}{2} = \frac{- 0.4}{2}

化简

\frac{2 sin ( x - 1 0 ^{\circ} )}{2} : sin (x - 1 0^{\circ})

\frac{2 sin ( x - 1 0 ^{\circ} )}{2}

数字相除:

\frac{2}{2} = 1

= sin (x - 1 0^{\circ})

化简

\frac{- 0.4}{2} : - 0.2

\frac{- 0.4}{2}

使用分式法则:

\frac{- a}{b} = - \frac{a}{b}

= - \frac{0.4}{2}

数字相除:

\frac{0.4}{2} = 0.2

= - 0.2

sin (x - 1 0^{\circ}) = - 0.2

sin (x - 1 0^{\circ}) = - 0.2

sin (x - 1 0^{\circ}) = - 0.2

使用反三角函数性质

sin (x - 1 0^{\circ}) = - 0.2

sin (x - 1 0^{\circ}) = - 0.2

的通解

sin (x) = - a \Rightarrow x = arcsin (- a) + 36 0^{\circ} n, x = 18 0^{\circ} + arcsin (a) + 36 0^{\circ} n

x - 1 0^{\circ} = arcsin (- 0.2) + 36 0^{\circ} n, x - 1 0^{\circ} = 18 0^{\circ} + arcsin (0.2) + 36 0^{\circ} n

x - 1 0^{\circ} = arcsin (- 0.2) + 36 0^{\circ} n, x - 1 0^{\circ} = 18 0^{\circ} + arcsin (0.2) + 36 0^{\circ} n

解

x - 1 0^{\circ} = arcsin (- 0.2) + 36 0^{\circ} n : x = - arcsin (\frac{1}{5}) + 36 0^{\circ} n + 1 0^{\circ}

x - 1 0^{\circ} = arcsin (- 0.2) + 36 0^{\circ} n

化简

arcsin (- 0.2) + 36 0^{\circ} n : - arcsin (\frac{1}{5}) + 36 0^{\circ} n

arcsin (- 0.2) + 36 0^{\circ} n

arcsin (- 0.2) = - arcsin (\frac{1}{5})

arcsin (- 0.2)

= arcsin (- \frac{1}{5})

利用以下特性:

arcsin (- x) = - arcsin (x)

arcsin (- \frac{1}{5}) = - arcsin (\frac{1}{5})

= - arcsin (\frac{1}{5})

= - arcsin (\frac{1}{5}) + 36 0^{\circ} n

x - 1 0^{\circ} = - arcsin (\frac{1}{5}) + 36 0^{\circ} n

将

1 0^{\circ}

到右边

x - 1 0^{\circ} = - arcsin (\frac{1}{5}) + 36 0^{\circ} n

两边加上

1 0^{\circ}

x - 1 0^{\circ} + 1 0^{\circ} = - arcsin (\frac{1}{5}) + 36 0^{\circ} n + 1 0^{\circ}

化简

x = - arcsin (\frac{1}{5}) + 36 0^{\circ} n + 1 0^{\circ}

x = - arcsin (\frac{1}{5}) + 36 0^{\circ} n + 1 0^{\circ}

解

x - 1 0^{\circ} = 18 0^{\circ} + arcsin (0.2) + 36 0^{\circ} n : x = 18 0^{\circ} + arcsin (0.2) + 36 0^{\circ} n + 1 0^{\circ}

x - 1 0^{\circ} = 18 0^{\circ} + arcsin (0.2) + 36 0^{\circ} n

将

1 0^{\circ}

到右边

x - 1 0^{\circ} = 18 0^{\circ} + arcsin (0.2) + 36 0^{\circ} n

两边加上

1 0^{\circ}

x - 1 0^{\circ} + 1 0^{\circ} = 18 0^{\circ} + arcsin (0.2) + 36 0^{\circ} n + 1 0^{\circ}

化简

x = 18 0^{\circ} + arcsin (0.2) + 36 0^{\circ} n + 1 0^{\circ}

x = 18 0^{\circ} + arcsin (0.2) + 36 0^{\circ} n + 1 0^{\circ}

x = - arcsin (\frac{1}{5}) + 36 0^{\circ} n + 1 0^{\circ}, x = 18 0^{\circ} + arcsin (0.2) + 36 0^{\circ} n + 1 0^{\circ}

以小数形式表示解

x = - 0.20135 \dots + 36 0^{\circ} n + 1 0^{\circ}, x = 18 0^{\circ} + 0.20135 \dots + 36 0^{\circ} n + 1 0^{\circ}

作图

流行的例子

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sin (2 x) = 0.8, - 18 0^{\circ} \leq x \leq 18 0^{\circ}

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